Review Questions Calculus

8/10/2019 Review Questions Calculus

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REVIEW

QUESTIONS MATH

214 FINAL EXAM

General Directin!" Read each question carefully. On your answer sheet, shade the letter thatcorresponds to your answer. #AL#ULATORS ARE NOT ALLOWED for thistest.

I$ TRUE OR FALSE$ Read each pair of statements carefully.S%a&e A, if statement 1 is TRUE and statement 2 isalso TRUE. S%a&e ', if statement 1 is TRUE butstatement 2 is FALSE. S%a&e #, if statement 1 isFALSE but statement 2 is TRUE. S%a&e D, ifstatement 1 is FALSE and statement 2 is also FALSE.

1. State(ent 1" If , then .

State(ent 2" If and f is a decreasing function, then .

2. State(ent 1" If and , then does not exist.

State(ent 2" If neither the nor exists, then does not exist.

3.State(ent

1"

d( tan2

x ) =dx

- 1

d(sec2

x )dx

- 1

State(ent 2" Du

tanh

u = Ducoth u

. State(ent 1"

State(ent 2" If f is differentiable,thend

dx

f ( x ) =

f '( x ).2 f ( x )

!. State(ent 1"

State(ent 2" sinh1 - cosh1 =1

e

II$ MULTI)LE #HOI#E$

". # $ath 21 student gi%es the following solution in an examination&

On which step did the student commit an error'#. (1) *. (3)+. (2) . -heres no error in the students solution.

Fr n*(+er! , t 1-. On the right is the graph of the function .

/. 0hat is '

#. *. 2+. 2 . does not exist

. 0hat is '

#. 3 *. cannot be+. - ¥ . does not exist

4. 0hat is '#. *. +¥

+. - ¥ . does not



1. 0here does ha%e a hole discontinuity'

#. +. *. .



11. 0hat is the %alue of '

1#.

6+. *. " . "

12. 0hat is the '

#. +. 1 *. 1 .

13. 0hat is the %alue of '

#. +. p*. p

2

. - 1p

2

1. 0hat is the first deri%ati%e of '

#. +. *. .

1!. 0hat is the first deri%ati%e of '

#. +. *. .

1". 0hat is the first deri%ati%e of , a is a constant'

#. +. *. .

1/. 0hat is if and '

#. +. *. .


#. *.

+. .


#. +. *. .

2. 0hat is the second deri%ati%e of '

#.+.

*..

21. 0hat is the fifth deri%ati%e of '

#. +. 1 *..

22. 0hat is if , '

#. +. *. .

2!. 0hat is the first

deri%ati%e of ycsc

1 x sec

1 x '

#.+. 1 *. .





3. 0hat is the equation of the line tangent to the cur%e at the point '

#. *.

+. .

3!. 0hat is the equation of the normal line to the cur%e at the point '

#. +. *. .

3"3/. ;or what nonnegati%e %alue(s) of b is the line normal to the graph of '

17 25 47 23#. +. *. .

2 3 6 3

3. # farmer wishes to fence in a rectangular field of 1, square feet. -he northsouth fences will

cost <1! per foot, while the eastwest fences will cost <" per foot. 0hat should the dimensions ofthe field be, eastwest side by north south side, so that the cost is minimi=ed'

#. ! ft by 2 ft +. 2 ft by ! ft *. 10 10 ft by 100 10 . 100 10 ft by 10 10

34. 0hat is the area of the largest rectangle that can be inscribed inside a semicircle with radius 1"'#. 1" sq.ft +. 32 sq.ft *. 21" sq.ft . 2!" sq.ft

. -he selling price P of an item is pesos, where x is the number of items produced

per day. If the cost * of producing and selling x items is pesos per day, how many

items should be produced and sold e%ery day in order to maximi=e the pro7t'#. 1! +. 1! *. 1 . 1

Fr n*(+er! 41 t 4/$#n automobile mo%es along a straight highway, with its position s gi%en by (s in feet, tin seconds).

1. 0hen is the car mo%ing to the right'

.#. +. *.

2. 0hen is the car decelerating'

.#. +. *.

3. 0hen does it change direction'

.#. +. *.

. # ladder 2 feet long leans against a house. #t what rate is the top of the ladder mo%ingdownward if the foot of the ladder is 12 feet away from the house and sliding along the groundaway from the house at the rate of 2 feet per second'

#. +. *. .

!. One end of an footlong trough is shown on the right. If water flows in at a rate of 2 ft3>min,

how fast is the surface rising when the water is 1ft deep'

#. *. +.

,.

". *ar # is tra%eling due west at ! :ph and car + is tra%eling due north at " :ph. +oth are headedfor the intersection of the two roads. #t what rate are the cars approaching each other when car# is .3 :m and car + is . :m from the intersection'



#. / :ph +. / :ph *. 1 :ph . 1 :ph

/. ;or which of the following functions is '

#.*.

+. ,.

4. 0hich of the following are the first partials of '

#. *.

+. .

!. 5i%en the function . 0hich of the following is '

#. *.

+. .

1. It is a quantity that cannot be changed through out the discussion.

a . variable b. Limits c. Constant d. Derivative

2. What is the derivative of any constant?

a. Infinity b. Zero c. ndefined d. 1

!. It is the "rocess of finding the derivative of a function.

a . Differentiation b. Integration c. #$ste" rule d. limits

#. Which among the follo%ing function is an im"licit function?

a. xy − x 2 + 4 y 2 = 4

b. c.

d.

&. If ' %hat is ?

a. 1 b. ( c. d.

). If ' %hat is ?

a. $ ! b. ! c. 1 d. (

*. What is the limit of as a""roached +!?

a. 1 b. 2 c. d.

,. What is the limit of as a""roaches +#?

a . b. c. d. undefined

-. What is the derivative of the square root of a function?

a. derivative of the function divided by the square root of the functionb. derivative of the function divided by t%ice the square root of the functionc. derivative of the function times t%ice the square root of the function

d. derivative of the function "lus t%ice the square root of the function

1(. n equation that consists of t%o functions in terms of another variable.

a. "arametric equation b. Im"licit function c. /0"licit function d.

"arameter

11. What is the derivative of ?

a. b. c. d.



12. What is the first derivative of the function ?

a. b. ( c. d.

1!. What is the derivative of ?

a . b. c. d.

1#. What is the first derivative of ?

a. b. c. d.

1&. What is the first derivative of ?

a. b. c. d.

1). What is the first derivative of ?

a . b. c. d.

1*. What is the equation of the tangent line to the curve at "oint ?

a. b. c. d.

1,. If ' %hat is the one value of 0 for %hich ?

a. b. c. ( d.

1-. What is the equation of the line tangent to the curve y = 3 x 2− 4 x and "arallel to the line ?

a . b. c. d.

2(. What is the 2nd derivative of the function ?

a. b. c. d.

21. What is the 1st derivative of the function ?

a. b. c. d.

22. If and ' %hat is ?

a . b. c. d.

2!. What is the 2nd

derivative of ?a. b.

c. !) d.

2#. What is the first derivative of ?

a. b. 1 c. $1 d. (

2&. What is the 2nd derivative of the function ?

a. b. c. d.

2). What is the !rd derivative of the function ?

a. b. c. 12 d.

2*. What is the 1st derivative of function ?

a. b. c. d.

2,. ind the if ?

a. b. c. d.

2-. What is the 2nd derivative of the function ?



a. b. c. d.

!(. What order derivative form of yields ?

a. 1st b. 2nd c. 3rd d. 4th

!1. What is the 2nd derivative of the function ?

a. b. c. d.

!2. What is the 1st derivative of the function ( x + y)2= 2ay ?

a. b. c. d.

!!. ind the 2nd derivative %hen ?

a. b. c. d.

!#. What is the 2nd derivative of function ?

a. b. d. d.

!&. What is the minimum "oint of the curve ?

a. $2'#) b. 2'$&( c. 2'$#) d. $2'$&(

!). What is the value of a and b res"ectively so that the curve %ill have a critical "oint at 32'&4?

a. !' - b. $!' $- c. $!' - d. !' $-

!*. What is the "oint %here the curve changes its sense of concavity?

a. 5a0imum "oint b. 5inimum "oint c. Curve tracing d. inflection "oint

!,. If the slo"e of the tangent line to the curve is !' %hat is the "oint of tangency?

a. b. c. d.

!-. What is the 2nd derivative of the function ?

a. b. c. d. 0

#(.What is the equation of the line normal to the curve at its "oint of inflection.

a. b. c. d.

#1. What are the t%o numbers %hose "roduct is 1(( and %hose sum is minimum?

a. 2( 6 & b. 2& 6 # c. 1( and 1( d. &( 6 2

#2. What are the t%o numbers %hose sum is !) and the "roduct of one by the square of the other is minimum?

a. 2# 6 12 b. 12 6 2# c. !( 6 ) d. ) 6 !(

#!. What number e0ceeds its square by the minimum amount?

a. b. c. 1 d. -1

##. What should be the sha"e of rectangular field of a given "erimeter if it is to have a ma0imum area?

a.rectangle

b.7quare

c.8riangle

d.circle

#&. rectangle is inscribed in the elli"se %ith its sides "arallel to the a0es of the elli"se. What are

the dimensions of the rectangle of minimum "erimeter %hich can be so inscribed?

a. 12 9 #, b. *2 0 , c. 2&) 0 ! d. 1, 0 !2

#). What are the t%o numbers %hose sum is a' and the "roduct of the square of one by the cube of the other is to

be a ma0imum?

a. b. c. d.



#*. If the hy"otenuse of a right triangle is given' %hat %ill be the resulting triangle if the area is ma0imum?

a. right triangle b. Isosceles triangle c. 7calene triangle d. equilateral

triangle

#,. right circular cylinder has a height of # cm. What is the rate of change of its volume %ith res"ect to a radius r of

its base?

a. b. c. d.#-. gutter having a triangular cross$section is to be made by bending a stri" of tin in the middle. What is the

angle bet%een the sides %hen the carrying ca"acity is ma0imum?

a. b. c. d.

&(. 8he %ord :derivative; means .

a. Limits b. differential calculus c. change d. function

0'UO MAN ANG )USO AT MALAAS ANG TIWALA

WALA RING MA)A)ALA UNG ULANG SA GAWA3

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Review Questions Calculus