Math201 Solved FinalE T113

7/30/2019 Math201 Solved FinalE T113

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Multiple Choice Part [90 pts] MASTER Page 6 of 13

Q1. A line contained in the tangent plane to the surface x2+2y2z2 = 5 at the point (2, 1, 1) is

(A) 2 x = y 12

=z 1

2

(B) x 2 = y 12

= z 12

(C)x 2

2=

y 12

= 1 z

(D)x 2

2=

y 12 = z 1

(E)x 2

2= y 1 = z 1

2

Q2. Given the parametric curve x = et, y = tet,d2y

dx2at the point (1, 0) is equal to

(A) 1

(B)1

e

(C) e

(D) 1 + e

(E) 1 +1

e


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Final Exam Math 201 (T-113) MASTER Page 7 of 13

Q3. The distance form the point P(2, 1, 4) to the plane which contains the points Q(1, 0, 0),R(0, 2, 0), and S(0, 0, 3) is equal to

(A)17

7

(B)15

7

(C)20

7

(D)13

7

(E)

16

7

Q4. The maximum increase of f(x,y,z) = tan(x + 2y + 3z) at the point (5, 1, 1) is in thedirection of

(A) 1, 2, 3

(B) 3, 2, 1

(C) 1, 2,3

(D) 3,2, 1

(E) 1, 2, 3


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Q5. The equation z2 = 9 +9

4r2 given in cylindrical coordinates describes a

(A) hyperboloid of two sheets

(B) hyperboloid of one sheet

(C) cone

(D) elliptic paraboloid

(E) hyperbolic paraboloid

Q6. The cartesian equation of the parametric curve x = 2cosh(t) , y = 5 sinh(t) is

(A) 25x2 4y2 = 100

(B) 25x2 + 4y2 = 100

(C) 4y2

25x2 = 100

(D) x2 + y2 = 100

(E) 4x2 + 25y2 = 100


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Q7. The parametric curve x = et cos(t), y = et3 sin(t) has

(A) a horizontal tangent line at t = 5/6 and a vertical tangent line at t = 5/4

(B) a horizontal tangent line at t = 2/3 and a vertical tangent line at t = /4

(C) a horizontal tangent line at t = 5/6 and a vertical tangent line at t = 3/4

(D) a horizontal tangent line at t = /4 and a vertical tangent line at t = /6

(E) a horizontal tangent line at t = /3 and a vertical tangent line at t = 7/6

Q8. If z =x + y

x y with x =8r

sand y =

r2 + s2, then

z

r

(r,s)=(3,4)

is equal to

(A) 645

(B) 30

(C)136

5

(D) 18

(E) 145


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Q9. Using Lower Left Corners with x = 1 and y = 2, the integral

R

(x + y) dA

over the region R = [0, 3] [1, 3] is approximately equal to

(A) 12

(B) 6

(C) 3

(D) 24

(E)17

2

Q10. The area inside the curve r = cos() and outside the curve r = 1 cos() is equal to

(A)

3 3

(B) 2

3 23

(C) 2 23

(D) 1 3

(E) 3 2

3


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Q11. Let 5x 2y 2z = 1 and 3x + y + z = 6 be two planes. If is the angle between theseplanes, then sin() is equal to

(A)

2

3

(B)

1

3

(C)

3

11

(D)

8

11

(E)

35

Q12. Let a be a vector of magnitude 2 whose direction angles with the positive x, y, and z-axesare /3, /4, and 2/3, respectively. Ifb is a unit vector so that the angle between a andb is /6, then proj

ab is

(A)

3

4 1,

2,1

(B)

31,2,1

(C)

3

41,2, 1

(D) 1,2,1

(E)141,2, 1


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Q13. The volume of the solid in the first octant bounded by the planes 3 x + 2y + z = 6 and3x + 2y + 6z = 6 is

(A)5

6

20

(63x)/20

(6 3x 2y) dydx

(B)1

6

20

30

(6 3x 2y) dydx

(C)1

6

30

(62y)/30

(6 3x 2y) dxdy

(D)5

6

20

(63x)/20

(1 3x 2y) dydx

(E)

5

630(62y)/30 (1 3x 2y) dxdy

Q14. If f(x, y) = sin

x

y

, then the limit

limy1

fx(, y) fx(, 1)y 1

is equal to

(A) 1

(B) 0

(C)

(D) 2

(E)


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Q15. An equation of the tangent plane to the surface z =

1 x2 y2 at the point of inter-section of the surface with the line

x

4=

y

2=

z5

is

(A) 4x + 2y +

5z 5 = 0

(B) 4x 2y + 5z 5 = 0

(C) x + y + z 3 = 0

(D) x + y + z+ 3 = 0

(E) 4x + 2y +

5z+ 5 = 0


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Correct Choices for Multiple Choice Questions

Questions MASTER CODE 001 CODE 002 CODE 003 CODE 004

1 A B D C E2 A A E D B3 A B C A C4 A D C C D5 A C A B C6 A C B E D7 A E D A B8 A D B B B9 A A A D A

10 A B C E E11 A E E C A12 A D E D D13 A C B B E14 A A A D A15 A B D E C

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Math201 Solved FinalE T113