001

$$$001

What property of determinant of a

matrix А is wrong?A) If A has a row (column) of zeros, then detA=0;B) If A has two identical rows (columns), then detA =0;C) If B is obtained by multiplying each element of matrix A by a scalar k; then detB=kdetA;D) If B is obtained by interchanging two rows (columns) of [A]; then [B]=-[A];E) If B is obtained by adding a multiple of a row (column) of A to another; then [B]=[A].{Correct answer} = C

$$$002

Complete the determinant of .

A) 11;B) –45;C) 36;D) 45;E) 63.{Correct answer} = D$$$003

Rank of a matrix would be only:

A) real number;B) decimal number(fraction);C) integer;D) natural number;E) complex.{Correct answer} = D

$$$004

Find the rank of the matrix:

A) 2;B) 1;C) 3;D) 4;E) 0.{Correct answer} = A

$$$005

What property doesn’t belong to elementary row operations?

A) Interchange the i-th row and the j-th row;B) Multiply the i-th row by a zero scalar k;C) Replace the i-th row by k times the j-th row plus the i-th row;D) Replace the i-th row by k times the j-th row plus k (nonzero) times the i-th row;

E) Delete the 0-row.{Correct answer} = B

$$$006

What system of vectors forms a basis in two-dimensional vector space?

A) system of 3-linear independent vectors;B) two noncollinear vectors;C) two collinear vectors:D) three noncomplaine vectors;E) three complain vectors.{Correct answer} = B

$$$007

Find the size of a matrix C, if it is known, that

·C= .

A) 42B) 32C) 24;D) 34;E) 24.{Correct answer} = A

$$$008

Let A, B be the non-square matrices of same size and let m, n be scalars. Which one of the following properties is wrong?

A) A+B=B+A;B) m(nA) = (mn)A:C) m(A+B) = mA+mB;D) (m+n)A = mA + nA;E) A(nB) = (nA)B = n(AB).{Correct answer} = E

$$$009

Find unknown matrix X from following equation: .

A) ;

B) ;

C) ;

D) ;

E) .

{Correct answer} = C

$$$010

What property of a matrix is wrong?

A) (k·A)T = k ·AT ,for any kK – scalar field;B) (A·B)T = AT·BT , if A has nm size and B has mk size;C) (A+B)T = AT + BT , if A and B have same sizes;D) (A-1)T = (AT)-1 , if A square and nondegenerate matrix;E) (AT)T = A.{Correct answer} = B

$$$011Find the eigenvalues of the matrix

(Matrices and matrix operations)A) 0, 0;B) 1, 1;C) 0, 1;D) 2, 0;E) 0, 3.{Correct answer} = C

$012Find the eigenvalues of the matrix

(Matrices and matrix operations)A) 1, 1;B) 1, 0;C) 1, 2;D) 2, 2;E) 0, 2.{Correct answer} = C


(Matrices and matrix operations)A) 0, 0;B) 1, 1;C) 1, -1;D) 1, 2;E) 0, 1.{Correct answer} = C


(Matrices and matrix operations)A) 1, 0, 0;B) 1, 1, 0;C) 1, 1, 1;D) 1, 1, 2;E) 2, 1, 2.{Correct answer} = C


(Matrices and matrix operations)A) 0, 0, 0;B) 1, 0, 0;C) 1, 1, 0;D) 1, 1, 1;E) 1, 2, 1.{Correct answer} = A

$$$016

What systems of linear equations are equivalent?

A) if systems have same matrix of coefficients attached to independent variables;B) if systems have same set of solutions;C) if systems have same associative homogeneous systems;D) if systems have same number of equations;E) if systems have same number of independent variables.{Correct answer} = B

$$$017What dimension of solution space of homogeneous system with 8 linear equations and 12 independent variables, if is known, that rank of matrix of the system is equal to 4?A) 8;B) 4;C) 12;D) 2;E) 10.{Correct answer} = A

$$$018

Let F: R5R5 be a linear mapping: dim(kerF)=2. Find dim(ImF).

A) 0;B) –2;C) 7;D) 3;

E) –3;{Correct answer} = D

$$$019

Express the vector from the point A(2, 3) to the origin in the form ai + bj.

A) -2i + 3j;B) 2i + 3j;C) -2i – 3j;D) –i + 1.5j;E) 2i – 3j.{Correct answer} = C

$$$020

Find the unit vector that is tangent to the curve 3x2+8xy+2y2–3=0 at point (1, 0).

A) - i + j;

B) i + j;

C) - i + j;

D) i - j;

E) i - j.

{Correct answer} = D

$$$021Express the vector i + j as a product of its length and direction.

A) 2( i + j)

B) 2( i - j)

C) -2( i + j)

D) 2( i + j)

E) i + j

{Correct answer} = A

$$$022

Express the vector i+4j-8k as a product of its length and direction.

A). 4[i+4j-8k];B). 4[(1/4)i+j-2k];C). 9[(1/9)i+(4/9)j-(8/9)k];D). –9[(1/9)i+(4/9)j-(8/9)k];E). 8[(1/8)i+(1/2)j-k].{Correct answer} = C

$$$023

Find scalar (or inner, in other terminology) product AB of vectors A and B if A=5j-3k, B=i+j+k.

A). 0;B). –2;C). 4;D). 3;E). 2.{Correct answer} = E

$$$024

Find the cross product AB of vectors A and B if A=i-k and B=j+k.

A). 3i-j+k;B). i-j+k;C). i+2j+k;D). –i-j+k;E). i-j-k.{Correct answer} = B

$$$025

Which one of the sets below is not a vector space?

A) the set of all n-tuples of elements of K – an arbitrary scalar field with vector addition and scalar multiplication.

B) the set of all mn matrices with entries from an arbitrary scalar field with respect to the operations of matrix addition and scalar multiplication;

C) the solution space of homogeneous linear equation system;

D) the solution space of nonhomogeneous linear equation system;

E) the set of polynomials a0+a1t+a2t2+…antn with respect to the usual operations of addition of polynomials and multiplication by constant.


$$$026

What is the relationship between the dimension of a linear space and the number of elements in a basis of the same space?

A) number of elements in basis is less then the dimension of vector space;B) number of elements in basis is larger then the dimension of vector space;C) number of elements in basis is equal to dimension of vector space;D) number of elements in basis is less or equal then the dimension of vector space;E) number of elements in basis is larger or equal then the dimension of vector space.{Correct answer} = C

$$$027

How many bases are contained in every nonzero vector space?

A) a single;B) two;C) hundred;D) infinite number;E) number of bases is equal to dimension of vector space;


$$$028

Let e1,e2,…en is an arbitrary system of vectors of a vector space V. This system is basis in V if :

A) e1,e2,…en is system of linear independent vectors;B) e1,e2,…en is set of orthonormal vectors;C) number of vectors in this system is equal to dimension of V;D) e1,e2,…en is system of linear independent vectors and n is equal to dimension of V;E) e1,e2,…en is set of normal vectors.{Correct answer} = D

$$$029

What mapping is linear?

A) F: R2→R defined by F(x,y)=xy;B) F: R2→R3 defined by F(x,y)=(x+2, 3x, 2x+y);C) F: R2→R2 defined by F(x,y)=(x, lny);D) F: R3→R3 defined by F(x,y,z)=(x-y, y+z, z2);E) F: R3→R defined by F(x,y,z)= -x+3y+5z.{Correct answer} = E

$$$030

Let F: R3→R2 and G: R2→R2 be the linear mappings. Find possible composition from them, if F(x,y,z)=(2y,x+z) and G(x,y)=(x-y,x+3y):

A) (G◦F)(x, y, z)=(2y-x-z, 2y+3x+3z);B) (G◦F)(x, y, z)=(2x-y-z, 2x+3y+3z);C) (F◦G) (x, y) = (2y-x-z, 2y+3x+3z);D) (F◦G)(x, y, )=( 2x+6y, 2x+2y);E) (G◦F)(x, y, z)=(2y-x-z, 2y+3x+3z) and (F◦G)(x, y )=( 2x+6y, 2x+2y).{Correct answer} = A

$$$031

Suppose U and W are subspaces of R7. Let dimU=3, dimW=4, dim(U+W)=6. Find dim(UW).

A) 0;B) 2;C) –1;D) 1;E) 3.{Correct answer} = D

$$$032

Express the vector from the point A(4, 3) to the origin in the form ai + bj.

A) –4i + 3j;B) 4i + 3j;C) –4i – 3j;

D) –i – j;

E) 4i – 3j.{Correct answer} = C

$$$033

Find the unit vector that is normal to the curve 3x2+8xy+2y2–3=0 at point (1, 0).

A) - i + j;

B) i + j;

C) - i + j;

D) i + j;

E) i - j.


$$$034Express the vector i + 4j as a product of its length and direction.

A) 5( i + j);

B) 5( i – j);

C) -5( i + j);

D) -5( i + j);

E) -3i - 4j.{Correct answer} = A

$$$035

Express the vector i-4j+ k as a product of its length and direction.

A) 4[i-4j+ k];B) 4[(1/4)i-j+ k];

C) 5[(1/5)i-(4/5)j+ k];

D) –5[(1/5)i-(4/5)j+ k];

E) [i-4j+ k].{Correct answer} = C

$$$036

Find scalar (or inner, in other terminology) product AB of vectors A and B if A=5j+3k,

B=2i-3j+k.

A). 23;B). 19;C). 0;D). -2;E). -12.{Correct answer} = E

$$$037

Find the cross product AB of vectors A and B if A=2i+k and B=i+j+k.

A). 2i+j+k;B). -i-j+2k;C). i+j+2k;D). 2i+j+2k;E). i+j-2k.{Correct answer} = B

$$$038Find the length of the vector a=(1, 3)R2

A) 1;B) 3;C) ;

D) ;E) 5.{Correct answer} = C

$$$039Find the length of the vector a=(1, 1)R2

A) 2;B) 1;C) ;

D) ;E) 4.{Correct answer} = C

$$$040Find the length of the vector a=(1, 1, 0)R3

A) 3;B) 1;C) ;D) 2;E) 4.{Correct answer} = C

$$$041Find the length of the vector a=(1, 2, 3)R3

A) ;B) 6;C) 10;D) 2;E) 7.{Correct answer} = A

$$$042Find the angle between two vectors a=(0, 1)R2, and b=(1, 0)R2

A) ;

B) ;

C) ;

D) ;

E) - .{Correct answer} = B

$$$043Find the angle between two vectors a=(1, 1)R2, and b=(1, 0)R2

A) - ;

B) ;

C) ;

D) ;

E) .

{Correct answer} = B

$$$044Find the angle between two vectors a=(1,0,0)R3, and b=(0, 0, 1)R3

A) ;

B) ;

C) ;

D) 0;E) .{Correct answer} = A


A) ;

B) ;

C) ;

D) ;

E) .{Correct answer} = D


A) ;

B) ;

C) ;

D) 0;

E) .


$$$047Which two vectors are orthogonal?A) (1, 1), (2, 2);B) (1, 0), (0, 1);C) (1, 3), (3, 1);D) (1, 2), (2, 4);E) (1, 1), (1, 3).{Correct answer} = B

$$$048Which two vectors are orthogonal?A) (1, 2), (-2, 1);B) (1, 1), (3, 3);C) (1, 3), (2, 6);D) (2, 2), (2, 4);E) (3, 3), (6, 6).{Correct answer} = A

$$$049Which two vectors are orthogonal?A) (1, 0, 0), (1, 1, 1);B) (1, 0, 0), (0, 0, 1);C) (1, 0, 1) , (2, 0, 2);D) (1, 1, 1) , (2, 2, 2);E) (1, 2, 2) , (2, 1, 1).{Correct answer} = B

$$$050Which two vectors are orthogonal?A) (1, 1, 2), (1, 1, -1);B) (1, 1, 1), (1, 1, 2);C) (1, 2, 1), (1, 3, 1);D) (1, 2, 2), (1, 1, 2);E) (0, 0, 1), (1, 1, 1).{Correct answer} = A

$$$051Which two vectors are linearly independent?A) (1, 0), (0, 1);B) (1, 2), (2, 4);C) (1, 1), (2, 2);D) (3, 1), (6, 2);E) (0, 0), (1, 1).{Correct answer} = A

$$$052Which two vectors are linearly dependent?A) (1, 1), (1, 2);B) (1, 2), (2, 4);C) (0, 1), (1, 0);D) (2, 1), (1, 2);E) (0, 1), (1, 1).{Correct answer} = B

$$$053

Choose the inequalities that describe the solid cube in R3 in the first octant bounded by the planes x = 2, y = 3, z = 3 (including planes themselves).

A) -2x0, -3y0, -3z0B) 0x2, 0y3, 0z3C) -2x2, -3y3, -3z3D) -3x2, -2y3, -3z3E) 0<x<2, 0<y<3, 0<z<3{Correct answer} = B

$$$054

Find the equation for the line in the xy-plane that passes through the point P(-1,2) perpendicular to the vector (-2i-j).

A). x-2y=0;B). –x+2y=0;C). x+2y=0;D). –2x-y=0;E). –2x+y=0.{Correct answer} = D

$$$055

Find the ellipse’s standard-form equation if its Foci: ( , 0) and vertices: (2,0)

A). x2/4+y2/2=1;B). x2/4-y2/2=1;C). x2/2+y2/4=1;D). x2/2-y2/4=1;E). x2+2y2=4.{Correct answer} = A

$$$056

Find parametric equation for the line through (0, -7, 0) perpendicular to the plane x+2y+2z=13.

A). x=1, y=2-7t, z=2;B). x=t, y=-7+2t, z=2t;C). x=-t, y=7-2t, z=-2t;D). x=-t, y=-7+2t, z=-2t;E). x=1, y=2+7t, z=2.{Correct answer} = B

$$$057

Choose the inequalities that describe the solid cube in R3 in the first octant bounded by the planes x=5, y=3, z=3 (including planes themselves).

A) -5x0, -3y0, -3z0;B) 0x5, 0y3, 0z3;C) -2x5, -3y3, -3z3;D) -5x2, -3y3, -3z3;E) 0<x<5, 0<y<3, 0<z0.{Correct answer} = B

$$$058

Find the equation for the line in the xy-plane that passes through the point P(1,-2) perpendicular to the vector (-2i+3j).

A) x-2y=0;B) –2x+3y=0;C) 2x-3y=0;D) –2x+3y+8=0;E) 2x-3y+1=0.{Correct answer} = D

$$$059

Find the ellipse’s standard-form equation if its Foci: (0, ) and vertices: (0,2)

A) x2/2+y2/4=1;B) x2/2-y2/4=1;C) x2/4+y2/2=1;D) x2/2-y2/4=1;E) x2+2y2=4.{Correct answer} = A

$$$060

Find parametric equation for the line through (0, 1, 2) perpendicular to the plane 2x+y+z=13.

A) x=1, y=2-7t, z=2;B) x=2t, y=1+t, z=2+t;C) x=-t, y=1-t, z=-t;D) x=-2t, y=1+2t, z=-t;E) x=0, y=1, z=2.{Correct answer} = B

$$$061

Find limy2((y2+5y+6)/(y+2))

A) 1;B) 3;C) –5;D) 5;E) 0.{Correct answer} = D

$$$062

Find limx-3((x+3)/(x2+4x+3)).

A) –2;B) –1/4;C) 1/4;D) 0;

E) –1/2.{Correct answer} = E

$$$063

Find limx∞(7x3/(70x3-4x+1)).

A) ∞;B) 0;C) 1/10;D) –1/10;E) 1/70.{Correct answer} = C

$$$064

Find limx∞(x2/(x3-4x+1)).

A) 2;B) –1;C) 1;D) ∞;E) 0;{Correct answer} = E

$$$065

Find limx0(sin3x/7x).

A) 7/3;B) 3/7;C) 0;D) ∞;E) 1.{Correct answer} = B

$$$066

Find limx∞(cosx/2x).

A) 0;B) 1;C) ∞;D) 1/2;E) 2.{Correct answer} = A

$$$067

Find limx0(1+2x)1/x.

A) 0;B) ∞;C) e½;

D) e2;E) 1.{Correct answer} = D

$$$068

Which of the following functions grow at the same rate as lnx as x.

A) 1/x;B) e-x;C) log2x2;D) 2;E) ex;{Correct answer} = C

$$$069

Find limy1((y2+2y-3)/(y+1))

A) 1;B) 3;C) 2;D) 0;E) 5.{Correct answer} = D

$$$070

Find limx2((x2-x-2)/(x-2)).

A) 2;B) 0;C) 1;D) ∞;E) 3.{Correct answer} = E

$$$071

Find limx∞(3x2/(2x2-4x+2)).

A) ∞;B) 0;C) 3/2;D) –3/2;E) 3.{Correct answer} = C

$$$072

Find limx∞(x3/(x4-3x+1)).

A) 1;B) –1;C) ∞;D) -3;E) 0.{Correct answer} = E

$$$073

Find limx0((sin4x)/6x).

A) 3/2;B) 2/3;C) 0;D) ∞;E) 1.


$$$074

Find limx∞((sinx)/3x).

A) 0;B) 1;C) ∞;D) 1/3;E) 3.{Correct answer} = A

$$$075

Find limx0(1+x)1/2x.

A) 0;B) ∞;C) e2;D) e½;E) 1.{Correct answer} = D

$$$076

Which of the following functions grow at the same rate as lnx2 as x.

A) 1/x;B) e-x;C) log2x3;D) 2;E) ex.{Correct answer} = C

$$$077

Find the limit of the sequence

A) 1;B) 1/2;C) 0;D) –1/2;E) 2;{Correct answer} = D

$$$078


A) 1;B) 0;C) 1/2;D) –1;E) .{Correct answer} = B

$$$079


A) 2;B) ;C) ;D) ;E) 1.{Correct answer} = C

$$$080


A) ;B) 0;C) 1;D) –1;E) .{Correct answer} = B

$$$081


A) 0;B) 2;C) 1;D) does not exist;E) -1.{Correct answer} = D

$$$082What value should be assigned to the parameter a to make the function

continuous at x=3.A) 3/2;B) 4/3;C) 6;D) 0;E) 5/3.{Correct answer} = B

$$$083

Find the points at which the function

is not continuous.

A) {0, 1, 2};B) {0, 2};C) 1;D) 0;E) 2.{Correct answer} = B

$$$084What value should be assigned to the parameter a to make the functionf(x)=continuous at x=1.A) -1;B) 1;C) 2;D) 0;E) 3.{Correct answer} = B

$$$085

Find the points at which the function

f(x)=

is not continuous.

A) {0,1,2};B) {1,2};C) 1;D) 2;E) 0.{Correct answer} = B

$$$086

Find the limit of the function

A) 0;B) 1;C) 3;D) 3/2;E) 2.{Correct answer} = D

$$$087


A) 1;B) 0;C) 2;D) ;E) –1.{Correct answer} = C

$$$088


A) ;B) 1;C) 0;D) –1;E) .


$$$089


A) 1;B) 3;C) ;D) 4;E) .{Correct answer} = E

$$$090


A) ;B) 0;C) 1;D) –1;E) 2.{Correct answer} = B

$$$091


A) 1;B) 0;C) 2;D) ;E) 10.{Correct answer} = B

$$$092


A) ;B) 2;C) 0;D) ;E) 5;{Correct answer} = C

$$$093


A) 0;B) 1;C) 5;D) ;E) .{Correct answer} = B

$$$094

Find dy/dx if y=(x+1)(3-x2).

A) 6x+2;B) 3x-x2;C) x+1;D) 3-x2;E) –3x2-2x+3.{Correct answer} = E

$$$095

Find dy/dx if y=

A) 2x2+7;B) (2x-7)x;C) (2x4+1)/x2;D) 2x+1/x2;E) (2x+7)/x.{Correct answer} = D

$$$096

Find dy/dx if y=

A) 2x/3;B) x2-4;C) (x2+x+4)/(x+0.5)2

D) (x2-4)(x+0,5);E) 2x(x+0,5).{Correct answer} = C

$$$097

Find dy/dx if y=(sin2x2)

A) xcos2x;B) 4xcos2x;C) 4xcos2x2;D) cos2x2;E) sin2x.{Correct answer} = C

$$$098

Find dy/dx if y=(1+x-1/x)-4

A) –4(1+x-1/x)-5(1+1/x2);B) –4(1+x-1/x)(1+1/x2);C) –4(1+x-1/x)-3;D) –4(1+x-1/x);E) –4(1+1/x2)-5

.


$$$099

Find dy/dx if y=x2cosx

A) -2xsinx;B) -x2sinx;

C) 2xcosx-x2sinx;D) 2xcosx+x2sinx;E) 2xcosx.{Correct answer} = C

$$$100

Find dy/dx if y=csc(x2+7x)

A) csc(2x+7)cot(2x+7);B) –(2x+7)csc(x2+7x)cot(x2+7x);C) csc(x2+7x)cot(x2+7x);D) (x2+7x)csc(2x+7);E) csc(x2+7x)cot(x2+7x)(2x+7).{Correct answer} = B

$$$101

Find dy/dx if y=(x2-2x+2)ex

A) (4x-4)e2x;B) 2(x2-2x+2)e2x;C) (2x-2)e2x;D) exx2;E) (2x-2)2xe2x-1.{Correct answer} = D

$$$102

Find dy/dx if y=cos(e-2x)

A) sin(e-2x);B) cos(e-2x2x);C) 2e-2xsin(e-2x);D) e-2x cos(e-2x);E) 2sin(e-2x).{Correct answer} = C

$$$103

Find dy/dx if 2xy+y2=x+y

A) (2x+2y-1)/(1-2y);B) (2x+2y+1)/(1+2y);C) (1+2y)/(2x+2y+1);D) (1-2y)/(2x+2y+1);E) (1-2y)/(2x+2y-1).{Correct answer} = E

$$$104

Find dy/dx if y=ln(3xe-x)

A) e-x(1-x)/x;B) e-x(1+x)/x;C) (1-x)/x;D) (1+x)/x;E) 1/(3xe-x).{Correct answer} = C

$$$105

Find dy/dx if lny=eysinx

A) (y2eycosx)/(1+yeysinx);B) (yeycosx)/(1-yeysinx);C) (yeycosx)/( 1+eysinx);D) eysinx+eycosx;E) eysinx-eycosx.{Correct answer} = B

$$$106

Find dy/dxif y=(x+3)(2-x2).

A) 3 x2+6x-2;B) 2-x2;C) x+3;D) 0;E) –3x2-6x+2.{Correct answer} = E

$$$107

Find dy/dx if y=

A) 2x+4;B) (2x-7)/x;C) (2x3+4)/x2;D) 1-1/x2;E) (4x+1)/x.{Correct answer} = D

$$$108

Find dy/dx if y=

A) 3x2/ (x+1)2;B) 3x2;C) (2x3+ 3x2+4)/(x+1)2;D) (x3-4)(x+1);E) (x3 -4)(x+1).{Correct answer} = C$$$109

Find dy/dx if y=(sin4x3)

A) x2cos4 x3;B) cos 12 x2;C) 12 x2cos4x3;D) sin4x3;E) cos 12x.{Correct answer} = C

$$$110

Find dy/dx if y=(1+x+x3)-3

A) –3(1+x+x3)-4(1+3x2);B) –3(1+x+x3) (1+3x2);

C) 3(1+x+x3)-2(1+3x2);D) –4(1+x+x3);E) (1+3x2)-3.


$$$111

Find dy/dx if y=x2sinx

A) 2xsinx;B) x2cosx;C) 2xsinx+x2cosx;D) 2xcosx+x2sinx;E) 2xcosx.{Correct answer} = C

$$$112

Find dy/dx if y=sec(x2+2x)

A) sec(2x+2)tan(2x+2);B) sec(x2+2x)tan(x2+2 x)( 2x+2);C) sec(x2+2x)tan(x2+2x);D) csc(2x+2);E) csc(x2+2x) (2x+2).{Correct answer} = B

$$$113

Find dy/dx if y=(x3+1)ex

A) 3x2ex;B) ex(x3+1);C) 3x2+1;D) (x3+3x2+1)ex;E) 3x2ex-1.{Correct answer} = D

$$$114

Find dy/dx if y=(sinx)x

A) x(sinx)x-1;B) x(cosx)x-1;C) (sinx)x(lnsinx+(xcosx)/sinx);D) x(sin)x(lnsinx-cosx);E) -x(sinx)x.{Correct answer} = C

$$$115

Find dy/dx if 3xy+y2=x+2y

A) (3x+2y)/(1+2y);B) (3x+2y+2)/(1-3y);C) (3x+2y)/(x+2);D) (3x+y2)/(x+2y);E) (1-3y)/(3x+2y-2).{Correct answer} = E

$$$116

Find dy/dx if y=ln(2x2e-2x)

A) e-2x(2-2x)/x;B) e-2x(2+2x)/x;C) (2-2x)/x;D) 4xe-3x;E) 1/( 2x2e-2x).{Correct answer} = C

$$$117

Find dy/dx if lny=eycosx

A) (eysinx)/( ey+1);B) (yeysinx)/(yeycosx-1);C) 1/y + eycosx;D) eycosx-eysinx;E) lny-eysinx.{Correct answer} = B

$$$118

Which of the following functions defined on appropriate interval does not satisfy Rolle’s theorem hypotheses.

A) y=x3-3x;B) y=cos(x);C) y=2x(2-cosx)2;D) y=1-x;E) y=2x3+3x2+x+1.{Correct answer} = D

$$$119Find dy/dx if y=

A) (6x-7);

B) ;

C) (6x5-7);

D) (ln2)ּ (6x5-7);

E) (x6-7x) .{Correct answer} = D

$$$120

Find dy/dx if y=(cosx)x

A) x(cosx)x-1;B) x(sinx)x-1;C) -(sinx)x;D) (cosx)x(lncosx+(xsinx)/x);E) (cosx)x(lncosx-(xsinx)/cosx).{Correct answer} = E

$$$121

Find the value of the estimate df=f(x0)dx, if f(x)=x3-x, x0=1, dx=0,1

A) 0,4;

B) 0,2;C) 0;D) 0,3;D) 0,1.{Correct answer} = B

$$$122

Write the differential formula that estimates the change in the volume V=r2h of a right circular cylinder when the radius changes from r0 to r0+dr and the height does not change

A) 2r0drB) r0hdr;C) 2r0hdr;D) r0hdr;E) 2r0hdr.{Correct answer} = C

$$$123

Find the intervals where the function y=x3-3x-4 increases

A) (-;-1)(1; +);B) (-1;1);C) (-1;0);D) (-;-1)(0; +);E) (-;1).{Correct answer} = A

$$$124

Find the point of inflection of the function y=4+3x-x3

A) no;B) 1/2;C) 4;D) 3;E) 0.{Correct answer} = E

$$$125

Find all points of local maxima and minima for y=2x4-4x2+1

A) x=0 a local minimum;B) x=1 local minimums;C) at x = 1 there are local maximums;D) at x= 1 there are local minimums and at x=0 a local maximum;E) no.{Correct answer} = D

$$$126

Find the points of maxima and minima for y=(x-8)2/3.

A) x=8, maxima;B) x=8, minima;C) x=-8, maxima;D) x=-8 minima;E) no.


$$$127

Find the intervals where the function y=2x3-3x2 decreases

A) (-;0)(1; +);B) (0,1);C) (-1,0);D) (-;-1)(0;+ );E) (- ;0).{Correct answer} = B

$$$128

Find the oblique asymptote of the graph of the function y=x2/(x-1).

A) y= –x+1;B) y=–x;C) y=x+1;D) y=x-1;E) y=x.{Correct answer} = C

$$$129Find the vertical asymptotes of the graph of the function y=(x2-4)/(x2-2).A) x= ;B) x=2;C) no;D) x= ;E) x= - .{Correct answer} = A

$$$130

Find

A) /2;B) 2;C) –2;D) 0;E) .{Correct answer} = C

$$$131

Find:

A) 1;

B) ;

C) 1/4;D) 0;

E) .


$$$132

Which of the following functions defined on appropriate interval does not satisfy Rolle’s theorem hypotheses.

A) y=x3-4x;B) y=cos(x);C) y=2x(2-cosx)2;D) y=2-x;E) y=x2-1.{Correct answer} = D

$$$133Find the intervals where the function y=x3/3-x2/2-2x decreases.A) (-∞; -1) (3; ∞);B) (1; 2);C) (1; 3);D) (-1; 2);E) (-∞; -1) (2; ∞).{Correct answer} = D

$$$134

Find the tangent line (y-y0)=f’(x0)(x- x0) to the function y = x3-x at the point x0=1

A) y=4x-1;B) y=x/2+1;C) y=-2x+1;D) y=-2x+2;E) y=2x-2.{Correct answer} = E

$$$135

Find the value of the estimate df=f(x0)dx, if f(x)=2x2-x, x0=1, dx=0.1

A) 0.4;B) 0.3;C) 0.2;D) 0;D) 0.1.{Correct answer} = B

$$$136

Find the maxima value of the function f(x)=-x2+2x-1 on the interval [0; 2]

A) 2;B) 1;C) 0;D) -1;E) -2.{Correct answer} = C

$$$137

Find the intervals where the function y=x2-2x+4 increases

A) (1; +);B) (-; -1)(0; +);

C) (-; -1)D) (-; 1);E) (-1; 1).{Correct answer} = A

$$$138

Find the point of inflection of the function y=5+6x2-x3

A) 1;B) 4;C) 3;D) 0;E) 2.{Correct answer} = E

$$$139

Find all points of local maxima and minima for y=x4/4-2x2+1

A) x=0 a local minimum;B) x=1 local minimums;C) at x = 1 there are local maximums;D) at x= 2 there are local minimums and at x=0 a local maximum;E) x=0 a local maximum.{Correct answer} = D

$$$140

Find the points of maxima and minima for y=(x-2)2/3.

A) x=2, maxima;B) x=2, minima;C) x=-2, maxima;D) x=-2 minima;E) x=-1 minima.{Correct answer} = B

$$$141

Find the intervals where the function y=2x3-6x2 decreases

A) (-; 0)(2; +);B) (0, 2);C) (-2, 0);D) (-; 0)(0; );E) (0; 1)(1; 2);{Correct answer} = B

$$$142

Find the oblique asymptote of the graph of the function y=2x2/(x-2).

A) y=2x;B) y=–2x;C) y=2x+4;D) y=-x+1;E) y=x.{Correct answer} = C

$$$143Find the vertical asymptotes of the graph of the function y=(x2-2)/(x2-4).A) x=2;B) x= ;C) x= ;D) x=2;E) x=-2.{Correct answer} = A

$$$144

Find

A) 1;B) 2;C) –1;D) 0;E) .{Correct answer} = C

$$$145

Find:

A) 1;

B) - ;

C) 1/9;D) 0;

E) .


$$$146

Evaluate

A) ;

B) +C;

C) 3x+ +C;

D) ;

E) 3x5/2+x2+C.


$$$147

Evaluate

A) ;

B) ;

C) t2/3+2t2+C;

D) +C;

E) .

{Correct answer} = E

$$$148

Evaluate

A) –3cos(t/3) + C;B) 3cos(t/3)+C;C) 1/3 cos(t/3)+C;D) -1/3cos(t/3)+C;E) sin(t/3)+C.{Correct answer} = A

$$$149

Express lim xk , where P is a partition of [0,1] as definite integral.

A) ;

B) ;

C) ;

D) ;

E) .


$$$150

Evaluate

A) ln|y2+25|+C;B) 2yln(y2-25)+C;

C) ln|y2

-25|+C;

D) 2ln(y2

-25)+C;

E) (y3

/3)-25y+C.


$$$151

Evaluate

A) 1;

B) 2;

C) 1-e;

D) 0;

E) e-1;


$$$152

Evaluate e-x

dx

A) –1;

B) 1;

C) 2;D) 3;

E) –3.{Correct answer} = B

$$$153

Evaluate

A) ;B) ;C) -1;D) -1;E) .{Correct answer} = A

$$$154

Evaluate

A) ;

B) ;

C) ;

D) 5ln5;E) 6ln5.{Correct answer} = C

$$$155Evaluate

A) tan10x2secx+C;

B) ((tan11x)/11)((sec3x)/3)+C;

C) 10tan9xsec2x+C;

D) ;

E). .


$$$156Evaluate (3x2+2)sec2(x3+2x)dx

A) ;

B) tan(x3+2x)+C;C) sec2(3x2+2)+C;D) cos2(x3+2x)+C;E) csc2(x3+2x).{Correct answer} = B

$$$157

Evaluate

A) 1/2;

B) -1- ;

C) ;

D) 1- ;

E) 0.{Correct answer} = D

$$$158Evaluate xcosxdx

A) ;

B) 2xsinx-cosx+C;C) -xsinx-cosx+C;D) -xsinx+cosx+C;E) xsinx+cosx+C.


$$$159Evaluate

A) ;

B) ;

C) ;

D) ;

E) 3x2lnx+C.{Correct answer} = B

$$$160

Evaluate

A) (5/2)sinxcosx+C;B) (5/2)sin3/2x3cos2x+C;

C) ;

D) ;

E) .


$$$161

Evaluate

A) ;

B) ;

C) ;

D) (3/2)(cos3/2xsinx)+C;

E) (3/2)(cos5/2x)+C.


$$$162

Evaluate:

A) ln(y2-2y-3)2+C;

B) (3/4)lny+3-(1/4)lny+1+C;

C) (1/2)lny2-2y-3+C;

D) lny2-2y-3+C;

E) (3/4)lny-3+(1/4)lny+1+C.


$$$163

Evaluate:

A) ;

B)

C)

D)

E) .{Correct answer} = B

$$$164

Evaluate:

A) ln3+lnx+C;B) ln3-lnx+CC) ln2+lnx+C;D) 2 ln2+lnx+C;E) 3 ln2+lnx+C.{Correct answer} = C

$$$165

Evaluate

A) 3;

B) +C;

C) 3x+2x2+C;D) ;E) 3x2+2x+C.


$$$166

Evaluate

A) ;

B) ;

C) ;

D) ;

E) .


$$$167

Evaluate

A) 1/3sin(3t) + C;B) 1/3sin(t/3)+C;C) 1/3cos(t/3)+C;D) 3sin(3t)+C;E) -3sin(3t)+C.{Correct answer} = A

$$$168

Evaluate

A) ln|sinx|+C;B) ln|cosx|+C;

C) ln|3-cosx|+C;

D) 2ln|3+cosx|+C;

E) tanx+C.


$$$169

Evaluate

A) 1;

B) 2;

C) 1-e8

;

D) 0;

E) e8

-1;


$$$170

Evaluate e-x

dx.

A) 1;

B) 2/3;

C) 0;D) 3;

E) 1/3.{Correct answer} = B

$$$171

Evaluate

A) ;B) ;C) ;D) ;E) .{Correct answer} = A

$$$172

Evaluate

A) ;

B) ;

C) ;

D) 3ln3;E) 6ln3.{Correct answer} = C

$$$173Evaluate

A) tan7x2secx+C;

B) ((tan8x)/8)((sec3x)/3)+C;

C) 7tan6xsec2x+C;

D) ;

E). .


$$$174Evaluate (6x5+2)sec2(x6+2x)dx

A) +C;B) tan(x6+2x)+C;C) sec2(x6+2x)+C;D) tan(6x5+2)+C;E) csc2(x6+2x)+C.


$$$175Evaluate

A) ;

B) 2xsinx+cosx+C;C) –xsinx+cosx+C;D) xcosx+sinx+C;E) –xcosx+sinx+C.{Correct answer} = E

$$$176Evaluate

A) ;

B) ;

C) ;

D) ;

E) 2xlnx+C.{Correct answer} = B

$$$177

Evaluate

A) 7sin6x +C;B) sin7x+cosx+C;

C) ;

D) 7sinx+C;

E) .


$$$178

Evaluate:

A) ;

B)

C) ;1

Cx

x

D)

E) .


$$$179

Evaluate:

A) ln2+lnx+C;B) ln2-lnx+C;C) ln3+lnx+C;D) 3 ln3+lnx+C;E) 3 ln2+lnx+C.{Correct answer} = C

$$$180

Suppose that . Find

A) –9;B) -39;C) 9;D) 39;E) 0.{Correct answer} = C

$$$181

Suppose that , . Evaluate

A) 0;B) –14;C) 14;D) –26;E) 26.{Correct answer} = E

$$$182

Find the area of the region enclosed by and y=2;

A) 32/3;B) 16;C) 32;D) 16/3;E) –16/3.{Correct answer} = A

$$$183

Find the area of the region enclosed by the line y=x and the curve

A) 10/3;B) 9;E) 7/2;D) 9/2;E) 6.{Correct answer} = D

$$$184

Find the volume of a solid generated by revolving about the x-axis the region bounded by the

line y=0 and curve y=x-x2 ( )

A) ;

B) ;

C) 1/30;

D) ;

E) .


$$$185

Express lim xk , where P is a partition of as definite integral.

A) ;

B) ;

C) ;

D) ;

E) .


$$$186Find the area of the region enclosed by y=x2+1; y=x2+3; x=1; x=2.A) 3;B) 0;C) 1;D) 2;E) -1.{Correct answer} = D

$$$187

Find the volume of a solid generated by revolving about x-axis the region bounded by the line

and the curve ( )

A) ;

B) ;C) ;

D) ;

E) 0.


$$$188

Find the area of the region enclosed by ; y=0; x=0; x=1

A) ¼;

B) 1;

C) 0;

D) ¾;

E) 5/4.


$$$189

Suppose that . Find

A) –9;B) 9;C) –6;D) 30;E) 0.{Correct answer} = C

$$$190

Suppose that , . Evaluate

A) -17;B) 0;C) 17;D) –33;E) 33.{Correct answer} = E

$$$191

Find the area of the region enclosed by ; y=0; x=0; x=1

A) 4/3;B) 1/3;

C) 1;D) 0;E) –2/3.{Correct answer} = A

$$$192

Find the area of the region enclosed by the line y=2x and the curve

A) 10/3;B) 9;E) 7/2;D) 9/2;E) 6.{Correct answer} = D

$$$193

Find the volume of a solid generated by revolving about the x-axis the region bounded by the

line y=0 and curve y=2x-x2 ( )

A) ;

B) ;

C) 1/15;

D) ;

E) .


$$$194

Solve the differential equation (3x+2y)dx+(2x+y)dy=0.

A) ;

B) ;

C) 3x+3y+xy=C;D) F(x;y)= ;E) 3x+y-2xy=C.{Correct answer} = A

$$$195

Solve the differential equation

A) ;B) F(x;y)= ;C) ;D) ;E) 2y+2x=C.{Correct answer} = C

$$$196

Determine the constant A such that the equation is exact.

A) 3;B) 0;C) 3/4;D) 1;E) 3/2.{Correct answer} = E

$$$197

Solve the differential equation

A) ;B) ;C) ;D) ;E) .{Correct answer} = D

$$$198

Solve the differential equation (y+2)dx+y(x+4)dy=0

A) ;B) ;C) ;D) ;E) .{Correct answer} = C

$$$199Solve the differential equation cscydx+secxdy=0A) tanx+coty=c;B) sin2x-cos2y=c;C) –cscy+secx=lnc;D) –cscycoty+secxtanx=c;E) sinx-cosy=c.{Correct answer} = E

$$$200Solve the differential equation dy/dx=(x+y)/xA) cx=e-y/x;B) cx=ey/x;C) cx=ex/y;D) cy=ex/y;E) cy=ex/y.{Correct answer} = B

$$$201Which integrating factor make the equation (xy2+y)dx-xdy=0 exact?A) sinx;B) 2y;C) 2x;

D) 1/y2;E) 1/y;{Correct answer} = D

$$$202Solve the differential equation exdy/dx+2exy=1A) y=e-x+ce-2x;B) y=ex+ce;C) y=e-x+c;D) y=e-2x+c;E) y=ex+ce2x.{Correct answer} = A

$$$203Solve the initial value problem for y as a function of x: dy/dx+2y=x, y(0)=1.A) y=x2/2+1/2;B) y=ex+ce;C) y=x-1/4+ce-2x;D) y=x-1/4e-2x+3/4;E) y=x/2-1/4+5/4e-2x.{Correct answer} = E

$$$204Solve the equation d2y/dx2+2dy/dx=0A) y=c1e2x+c2e4x;B) y=c1ex+c2;C) y=c1+c2e-2x;D) y=c1ex+c2e-2x;E) y=c1+c2

2x.{Correct answer} = C

$$$205Solve the equation d2y/dx2-4dy/dx+4y=0A) y=(c1x+c2)e2x;B) y=c1e2x+c2e4x;C) y=c1+c2e2x;D) y=c1+c2e4x;E) y=c1e-4x+c2e4x.{Correct answer} = A

$$$206Solve the equation d2y/dx2-2dy/dx+4y=0A) y=e-x(c1sin( x));B) y=ex(c1cos( x)+c2sin( x));C) y=ex(c1cos2x+c2sin2x);D) y=ex(c1x+c2);E) y=e-x(c1x+c2).{Correct answer} = B

$$$207Solve the initial value problem d2y/dx2-y=0, y(0)=1,y´(0)=-2A) y=cosx+2sinx;

B) y=cosx-2sinx;C) y=-ex+3e-x;D) y=-1/2ex+3/2e-x;E) y=c1ex+c2e-2x;{Correct answer} = D

$$$208Solve the initial value problem: y´´-4y=0, y(0)=0, y´ (0)=3A) y=3e2x-3e-2x;B) y=(1/2)e2x-(3/2)e-2x;C) y=(1/4)e2x-(1/4)e-2x;D) y=(1/2)e3x+(3/2*e-3x;E) y=(3/4)e2x-(3/4)e-2x.{Correct answer} = E

$$$209Solve the equation: y´´-3y´-10y=-3A) y=c1e5x+c2e-2x+3/8;B) y=c1e5x+c2e-2x+3/10;C) y=c1e-5x+c2e-2x-3/10;D) y=c1e-5x+c2e2x-3/10;E) y=c1e-5x+c2e-2x+3/10.{Correct answer} = B

$$$210Solve the equation y´´-y´=sinxA) y=c1+c2ex+1/2(cosx-sinx);B) y=c1ex+c2e-x+1/2(cosx-sinx);C) y=c1+c2ex+2(cosx-sinx);D) y=c1ex+c2e-x+3(cosx-sinx);E) y=c1+c2ex+sinx.{Correct answer} = A

$$$211The roots of the auxiliary equation, corresponding to a certain 10-th order homogeneous linear differential equation with constant coefficients are4, 4, 4, 4, 2+3i, 2-3i, 2+3i, 2-3i, 2+3i, 2-3i,Write the general solution.A) y=(C1+C2x+C3x3)e4x+e2xC4cos3x+e2xC5sin3x;B) y=C1e4x+C2e2x+ e2xC4cos3x+e2xC5sin3x;C) y=(C1+C2x+C3x2+C4x3)e4x+e2x((C5+ C6x+C7x2)cos3x+(C8+C9x+C10x2)sin3x);D) y=(C1+C2x)e4x+e2x((C5+C6+C7x2)cos3x+(C8+C9x)sin3x);E) y=(C1+C2x+C3x2+C4x3)e4x+e2x((C5+C6x+C7x2)cos3x.{Correct answer} = C

$$$212Find the general solution of the differential equation y´´-3y´+2y=4x2

A) y=c1ex+c2e2x+4x2;B) y=c1ex+c2e3x+2x2+6x;C) y=c1+c2e2x+2x2+6x+8;D) y=c1ex+c2e2x+2x2+6x+7;E) y=ex+e2x+2x2+2.


$$$213The general solution of the homogeneous linear differential equation y´´-2y´-3y=0 isyc=c1e3x+c2e-x.Find the particular solution of the equation y´´-2y´-3y=2ex.A) yp=2xex;B) yp=xex;C) yp=-(1/2)ex;D) yp=1/2e-x;E) yp=3ex.{Correct answer} = C$$$214

Let be a series of positive terms. Then series converge, if

A) exists and greater than 1;

B) exists and less than 1;

C) ;

D)

E) .


$$$215

Let be a series of positive terms. Then diverges, if

A) ;

B) exists and greater than 1, or is infinite;

C) exists and less than 1;

D) ;

E) .


$$$216


A) 1;B) 0;C) 2;D) –2;E) –1.{Correct answer} = E

$$$217

Determine if the following sequence converges or diverges:

A) converges to 3/4;B) converges to 0;C) converges to 4/3;D) diverges;E) converges to 1.{Correct answer} = B

$$$218Use the Limit Comparison Test to determine the convergence or divergence of the series

A) the test fails;B) the test does not apply;C) the series converges;D) the series diverges;E) the test is inconclusive.{Correct answer} = C

$$$219

Determine the convergence or divergence of the series using Ratio Test

A) the Ratio Test does not apply;B) the Ratio Test is inconclusive;C) diverges by the Ratio Test;D) converges by the Ratio Test;E) the Ratio Test fails.{Correct answer} = D

$$$220One of the following statements is not true

The following rules hold if =A and =B

A) lim[an+bn] = A+B;B) lim[an-bn] = A-B;C) lim[an·bn] = A·B;D) lim[k·bn] = k·B;E) lim[an/bn] = A/B.{Correct answer} = E

$$$221

Geometric series are series of the form a+ar+ar2+…+ arn-1+…= . One of the following

statements is not true:A) If |r|<1, the geometric series diverges;B) If |r|≥1, the geometric series diverges;

C) If |r|<1, the geometric series converges and =

D) =

E) If |r|<1, then rn0 as n{Correct answer} = A

$$$222Among the following statements choose the nth term test for divergence

A) If converges, then an0;

B) If 0, or if fails to exist, then diverges;

C) The series with no negative terms converges if there is a convergent series with

ancn for all n >n0, for some positive integer n0;

D) The series diverges if there is a divergent series of nonnegative terms with andn

for all n>n0;

E) Let an=f(n) where f(x) is a continuous, positive, decreasing function of x for all x1, then the

series and the integral both converge or both diverge.


$$$223

Choose the right answer for the series

A) converges conditionally;

B) fails to exist;

C) diverges;

D) converges;

E) diverges.


$$$224

Find the sum of the series

A) 1;B) 3;C) 2;D) 10;E) 4.{Correct answer} = C

$$$225

Which one of the following series does converge?

A) ;

B) ;

C) ;

D) ;

E) .


$$$226Which of the following series does converge?

A) ;

B) ;

C) ;

D) ;

E) .


$$$227Which one of the following series does converge conditionally?

A) ;

B) ;

C) ;

D) ;

E) .


$$$228

Which one of the following series does converge conditionally?

A) ;

B) ;

C) ;

D) ;

E) ;


$$$229Which one of the following series does converge absolutely?

A) ;

B) ;

C) ;

D) ;

E) ;


$$$230Which one of the following series does converge absolutely?

A)

B)

C)

D)

E)


$$$231Which one of the following series does diverge?

A)

B)

C)

D)

E)


$$$232Which one of the following series does diverge?

A)

B)

C)

D)

E)


$$$233

Express in the notation of

A) ;

B) ;

C) ;

D) ;

E) .


$$$0234

Find the sum of series

A) 7/3;B) 3/2;C) 1/2;

D) 4/5;E) 5/6.{Correct answer} = D

$$$235

Find the values of a1, a2, a3 and a4, if you know the formula of the n-th term an = of the

sequence {an}.

A) a1=-1,a2 =1/3, a3 =-1/5, a4=1/7;B) a1=1, a2 =3, a3=5, a4=7;C) a1=1, a2=-1/3, a3=1/5, a4=-1/7;D) a1=-1/3, a2=1/5, a3=-1/7, a4=1/9;E) a1=1/3, a2=-1/5, a3 =1/7, a4=-1/9.{Correct answer} = C

$$$236

Find the series radius and interval of convergence, if the formula for the n-th term is

A) 1, -1 x <1;B) for all x;C) 1, -1<x<1;D) 1, -1 x 1;E) 2, -2 x 1.{Correct answer} = C

$$$237

Find the series radius and interval of convergence, if the formula for the n-th term is .

A) , for all x;B) 1, 1<x<3;C) 4, -2<x<6;D) 0, x=2;E) 10, -8<x<12.{Correct answer} = E

$$$238

Find the radius of convergence of the power series

A) 0;B) 1;C) ;D) 10;E) 2.{Correct answer} = C

$$$239


A) 1;B) 5;C) 0;D) ;E) 2.{Correct answer} = A

$$$240


A) 0;B) 1;C) 2;D) 10;E) .{Correct answer} = B

$$$241

Find the interval of convergence of the power series

A) (-2,2);B) (-1,1);C) (0,1);D) (1,2);E) (0,+ ).{Correct answer} = B

$$$242


A) (-2, 2);B) (0, 1);C) (0, );D) (- , + );E) (-1,1).{Correct answer} = D

$$$243


A) (-1, 1);B) (0, 1);C) (-1, 0);D) (0, + );E) (1, 2).{Correct answer} = A

$$$244


A) (-1,1);B) (0,2);C) (0,1);D) (1,2);E) (-1,0).{Correct answer} = B

$$$245


A) (-1,1);B) (0,1);C) (- , + );D) (-1,0);E) (2,2).{Correct answer} = C

$$$246Find the Maclaurin series for the function f(x)=e-x

A) 1-x+x2/2!-x3/3!+x4/4!-……;B) 1+x+x2/2!+x3/3!+x4/4!+……;C) 2-x+x2/2!-x3/3!+x4/4!-……;D) 3-x+x2/2!-x3/3!+x4/4!-……;E) 4-x+x2/2!-x3/3!+x4/4!-……{Correct answer} = A

$$$247Find the Taylor polynomial of order 2 generated by f(x)=ln(x) at a=1A) P2(x)=x-(x-1)2;

B) ;

C) P2(x)=x+(x-1)2;

D) ;

E) P2(x)=x+(x-1)3.{Correct answer} = B

$$$248Find the Maclaurin series for the function f(x)=sinx

A) ;

B) ;

C) ;

D) ;

E)


$$$249Find the Maclaurin series for the function sin3x.

A) ;

B) ;

C) +…;

D) ;

E) .{Correct answer} = A

$$$250Find the Maclaurin series for the function cos(4x).

A) ;

B) ;

C) ;

D) ;

E) +…;{Correct answer} = C

$$$251

Find df/dx , if f(x,y)=(xy-1)4.

A) 4xy(xy-1)3;B) 2x(xy-1)5;C) 4x(xy-1)3;D) 4y(xy-1);E) 4(xy-1)3y.{Correct answer} = E

$$$0252

Find df/dy , if f(x,y)=exy .lny.

A) yexy.lny;B) xexy.lny+exy/y;C) xexy.lny;D) exy.lny+exy/y;E) exy/y.{Correct answer} = B

$$$253

Find df/dz ,if f(x,y,z)=yz·ln(xy).

A) yln(xy);B) zln(xy)+zx;C) y2z/x;D) yz/x;E) zln(xy).{Correct answer} = A

$$$254

Find , if f(x,y)=x2y+cosy+ysinx.

A) 2x-cosy+cosx;B) x2-siny+sinx;C) 2xy+ycosx;D) 2x+cosx;E) 2y-ysinx.{Correct answer} = D

$$$255Find f/z if ln(4x+2y+3z).

A) ;

B) ;

C) ;

D) ;

E) .


$$$256Find f/y if f(x,y)=( +(y/2))2/3

A) ;

B) ;

C) ;

D) ;

E) .


$$$257Find the function’s domain f(x,y)=lnx-lnyA) all (x,y);B) {(x,y):x0,y0};C) {(x,y):x0,y0};

D) {(x,y):x<0,y<0};E) {(x,y):x>0,y>0}.{Correct answer} = E

$$$258Find the function’s domain f(x,y)=A) all (x,y)B) {(x,y):yx}C) {(x,y):y>x}D) {(x,y):y<x}E) {(x,y):yx}{Correct answer} = B

$$$259Find the function’s domain and range if f(x,y)=ln(A) D:{(x,y)(0,0)}, R:{(-<z<+)};B) D:{all (x,y)}, R:{(-<z<+)};C) D:{all (x,y)}, R:{0,+ };D) D:{(x,y):x>0,y>0}, R:{(-<z<+)};E) D:{(x,y):x<0,y<0}, R:{0,+ }.{Correct answer} = A

$$$260

Find the function’s domain and range if f(x,y)=

A) D:{all (x,y)}, R:{z>0};B) D:{(x,y): y0, x0}, R:{(-<z<+)};C) D:{(x,y):x0}, R:{( -, +);D) D:{(x,y) :x0}, R:{z>0};E) D:{(x,y): y0, x0}, R:{z<0}.{Correct answer} = C

$$$261If three fight attendants who will staff a fight are randomly selected from a group of three male and four female flight attendants, what is the probability that all of those selected will be female?A) 1/33;B) 1/35;C) 2/35;D) 4/35;E) 3/35.{Correct answer} = D

$$$262Which of the following is NOT a possible probability?A) 25/100;B) 1.25;C) 1;D) 0;E) 0.13.{Correct answer} = B

$$$263It was estimated that 30% of all seniors on a campus were seriously concerned about employment prospects, 25% were seriously concerned about grades, and 20% were seriously concerned about both. What is the probability that a randomly chosen senior from this campus is seriously concerned about at least one of these two things?A) 0.30;B) 0.35;C) 0.40;D) 0.25;E) 0.55.{Correct answer} = B

$$$264Market research in a particular city indicated that during a week 18% of all adults watch a television program oriented to business and financial issues, 12% read a publication oriented to these issues, and 10% do both. What is the probability that an adult in this city, who watches a television program oriented to business and financial issues, reads a publication oriented to these issues?A) 6/7;B) 2/5;C) 1/3;D) 5/7;E) 5/9.{Correct answer} = E

$$$265A production manager knows that 5% of components produced by a particular manufacturing process have some defect. Six of these components, whose characteristics can be assumed to be independent of each other, were examined. What is the probability that none of these components has a defect?A) 0.056;B) 0.956;C) 0.9530.053;D) 0.9530.053;E) 0.9540.052.{Correct answer} = B

$$$266Determine the probability of getting exactly three heads in 6 tosses of a fair coin.A) 7/13;B) 4/13;C) 1/13;D) 5/14;E) 5/16.{Correct answer} = E

$$$267If the probability density function of a continuous random variable X is

then calculate the value of constant C.

A) 1/3;B) 1/2;C) 1/4;D) –1/2;E) –1/3.{Correct answer} = D

$$$268Compute the expected value of the discrete random variable described bythrowing a fair dice.A) 7/12;B) 7/3;C) 21/8;D) 5/3;E) 7/2.{Correct answer} = E

$$$269Suppose that the random variable T has the following probability distribution:

t 0 1 2P(T = t) 0.5 0.3 0.2

Compute E(T), the mean of the random variable T.A) 1.00;B) 1.20;C) 0.70;D) 2.1;E) 1.1.{Correct answer} = C

$$$270Let X be continuous random variable with probability density function

Find the expected value of random variable X.A) 12/7;B) 13/3;C) 27/4;D) 28/9;E) 19/3.{Correct answer} = D

Documents

001