mat 210 test 1 review (ch 10 and 11)diane/fall_2012/mat_210/choi... · 2012-10-05 · 1 mat 210...

1

MAT 210 TEST 1 REVIEW (Ch 10 and 11)

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Calculate the limit algebraically.

limx → +∞

9x6 + 4000x

3 + 2000000

12x6 + 8000x

3

a.1

12

b. −9

12

c.9

12

d. 12

e.11

12

2. Use a graph to determine whether the given

function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

g(x) =x − 4

x + 2

a. The point of discontinuity: 2.

b. The point of discontinuity: 0.

c. The function is continuous on its domain.

d. The points of discontinuity: -2, 0.

e. The points of discontinuity: 4,0.

3. At which labeled point is the slope of the tangent is

greatest?

a. P

b. R

c. Q

Name: ________________________ ID: A

2

4. Your Porche's gas mileage (in miles per gallon) is

given as a function M (x) of speed x in miles per

hour.

M(x) =10

x + 3,680x−1

Calculate M ' (x).

a.10

x +3,680

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

2

b.10

1 −3,680

x2

c.10x

x + 3,680

d.

10 1 −3,680

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x +3,680

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

2

e. -10(x

2− 3,680)

x2 + 3,680

Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃

2

5. Find the derivative of the function.

r(x) =2x

7−

x0.3

2+

4

7x1.3

− 4

a. r' (x) =2

7−

0.3x1.3

2−

5.2

7x0.3

b. r' (x) =2

7−

0.3x0.7

2+

5.2x2.3

7

c. r' (x) =2

7−

0.3

2x0.7

+5.2

7x2.3

d. r' (x) =2

7−

0.3

2x0.7

−5.2

7x2.3

e. r' (x) =2

7−

0.3

2x0.3

−5.2

7x1.3

6. For the cost function C(x), find the marginal cost at

the given production level x.

C(x) = 30,000 + 50x +1,000

x, x =500

a. $50.02 per item

b. $40.01 per item

c. $50.00 per item

d. $48.00 per item

e. $51.30 per item

7. If a stone is dropped from a height of Variable 972

isn't defined feet, its height after t seconds is given

by s = 972 − 20t2

. Find the stone's velocity at time t = 4.

a. v = 80 ft/s

b. v = 40 ft/s

c. v = 640 ft/s

d. v = 400 ft/s

e. v = 160 ft/s

8. At which labeled point is the slope of the tangent least (in the sense that -7 is less than 1)?

a. P

b. R

c. Q

Name: ________________________ ID: A

3

9. Calculate the average rate of change of the given

function over the interval 7, 8ÈÎÍÍÍ

˘˚˙̇˙ .

f (x) =x

2

7+

15

x

a.23

8

b.8

15

c.15

8

d.17

8

e.7

8

10. Use the graph to compute the given quantity.

limx→ 1

f (x)

a. 30b. + ∞

c. 12d. - ∞

e. 1

Name: ________________________ ID: A

4

11. The cost, in thousands of dollars, of airing x

television commercials during a Super Bowl game is given by the formula

C(x) = 100 + 1,500x − 0.004x2

.

Estimate how fast (in dollars per television

commercial) the cost is going up when x = 2.

a. $1,500,016

b. $1,499,984

c. $1,500

d. $1,499,992

e. $1,500


f (x) = e2x 6

ln8x

a. 12e2x 6

x5 ln8x +

e2x 6

x

b. 12e2x 5

x5 ln8x +

e2x 6

x

c. 12e2x 6

x6 ln8x +

8e2x 6

x

d. 12e2x 6

x5 ln8x +

e2x 6

8

e. 6e2x 6

x5 ln8x +

8e2x 6

x

13. If a stone is dropped from a height of 100 feet, its

height s after t seconds is given by s = 100 − 15t2

with s in feet.

a. Find the stone's velocity at t = 4 seconds.

b. When does it reach the ground, and how fast is it

travelling when it hits the ground?

Round your answers to the nearest hundredth.

a. -120, 6.67, -200.00

b. 120, 2.58, -77.46

c. -60, 1.29, -38.73

d. -8, 2.58, -200.00

e. -120, 2.58, -77.46

14. Calculate the derivative of the function.

s(x) =2x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

8

a. s ' (x) =2x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

730

(4x − 5) 2

b. s ' (x) = -82x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

730x

(4x − 5) 2

c. s ' (x) = -82x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

730

(4x − 5) 2

d. s ' (x) = 82x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

7

e. s ' (x) = -82x + 5

4x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

710

(4x − 5) 2

15. Estimate the limit numerically.

limx→3

x2

− 4

x − 3

a. 3b. -4c. -3d. - ∞

e. ∞

Name: ________________________ ID: A

5

16. The estimated marginal revenue for sales of ESU

soccer team T-shirts is given by

R ' (p) =(12 − 4p)e

−p2 + 6p

20,000,000

where p is the price (in dollars) the soccer player

charge for each shirt. Find R'(1), R'(3), R'(4).

Select the correct answer rounded to four decimal places.

a. R'(3) = 0.0001, R'(4) = 0, R'(1) = –0.0006

b. R'(1) = 0.0006, R'(3) = –0.0001, R'(4) = 0

c. R'(1) = –0.0006, R'(3) = 0, R'(4) = –0.0001

d. R'(1) = 0.0001, R'(3) = 0, R'(4) = –0.0006

e. R'(3) = 0.0001, R'(1) = 0, R'(4) = –0.0006


h (x) = e5x 2 − 6x + 1

x

a.10x

2− 6x − 1

xe

5x 2 − 6x + 1x

b.10x

3− 6x

2− 1

x2

e5x 2 − 6x + 1

x

c.5x

3− 12x

2− 1

xe

5x 2 − 6x + 1x

d.5x

3− 12x

2− 1

x2

e5x 2 − 6x + 1

x

e. none of these

18. Estimate dR

dp

|||p =16

of the function R =15

p.

a. -1

256

b. 15

c.15

256

d. -31

256

e. -15

256

19. Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a.

f (x) =x

2− 2x

x + 7; a = -7

a. 65b. 34c. 35d. 63e. No value of f (-7) will make it continuous at -7.

20. Find dx

dy using implicit differentiation.

(xy)2 + y2 = 9

a. -(x 2 + 1)

xy

b. -x

y

c.xy

(x 2 + 1)

d. 2y + 2x

e.xy

x2 + 1

Name: ________________________ ID: A

6

21. Find the equation of the straight line at right angles

to y = 3ex 2

at the point where x = 1.

a. y = -x

3e+

1

3e− e

b. y = -x

3e+

1

3e+ e

c. y =x

3e−

1

3e− e

d. y = -x

6e−

1

6e+ e

e. y = -x

6e+

1

6e+ 3e

f. none of these

22. Estimate dy

dx

||||x =4

of the function y = 6x2

.

a. 49

b. 46

c. 50

d. 52

e. 48

23. The cost of producing x teddy bears per day at the

Cuddly Companion Company is calculated by their marketing staff to be given by the formula

C(x) = 150 + 60x − 0.003x2

.

Evaluate the average cost C(250).

a. $15,149.25

b. $59.25

c. $60.15

d. $59.85

e. $14,962.50

24. Determine what, if any, value to assign to f(a) to

make f continuous at x = a.

f (x) =3

2x2

− x; a = 0

a. f (0) = -1

b. f (0) = 1

c. f (0) = 0

d. f (0) = -2

e. No value of f(0) will make it continuous at 0.

25. Estimate ds

dt

|||t=1

of the function s = 3t + t2

.

a. 7

b. 4

c. 10

d. 5

e. 2

26. Compute the indicated derivative using the chain rule.

y = 10x2

− 7x ;dx

dy

||||x =2

a.7

10

b.10

7

c.1

13

d. 2

e.1

33

Name: ________________________ ID: A

7

27. Calculate the average rate of change of the given function over the interval 2, 2.5ÈÎÍÍÍ

˘˚˙̇˙ .

p($) 2 2.5 3

q(p) (items) 300 200 350

a. 200

b. –100

c. –200

d. 1,000

e. –50

28. Compute f ' (2) .

f (x) =2.1

x

a. f ' (2) = 1

b. f ' (2) = 2.1

c. f ' (2) = 0.525

d. f ' (2) = -1.05

e. f ' (2) = -0.525

29. A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of

0.9 cm/day. How fast is the area growing when the

culture is 7 centimeters in radius? (The area of a

disc of radius r is A = π r2

.)

a.dA

dt= 25.2π

b.dA

dt= 21π

c.dA

dt= 1.8π

d.dA

dt= 6.3π

e.dA

dt= 12.6π

30. Compute f ' (a) algebraically for a = 3.

f (x) = 3x2 + x

a. 30

b. 19

c. 54

d. 57

e. 21


limx→+∞

6x4 + 40x

3

900x3 + 4

a. 0b. 6c. ∞

d. - ∞

e. 1

32. Compute the derivative function f '(x)

algebraically.

f (x) = -x2− 6x

a. f ' (x) = 2x − 6

b. f ' (x) = -x − 6

c. f ' (x) = -2

d. f ' (x) = -2x − 6

e. f ' (x) = -2x

Name: ________________________ ID: A

8

33. Use logarithmic differentiation to find dy

dx. Do not

simplify the result.

y = (7x + 1)(8x − 5)

a.dy

dx= (7x + 1)

7

7x + 1+

8

8x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

b.dy

dx= (7x + 1)(8x − 5)

7

7x + 1+

8

8x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

c.dy

dx= (8x − 5)

7

7x + 1+

8

8x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

d.dy

dx= (7x + 1)(8x − 5)

7

7x + 1+

8

8x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

2

e.dy

dx=

7

7x + 1+

8

8x − 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃


r (x) = ln(x 7)È

Î

ÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇

4

a.28[ln(x 7)]4

x7

b.28[ln(x 7)]3

x7

c.28[ln(x 7)]3

x

d.28[ln(x 6)]3

x7

e. none of these

35. Find the indicated derivative.

y = 6x3 +

4

x, x = 18 when t = 1,

dx

dt

|||t=1

= 2;dy

dt

||||t=1

= ?

Please round the answer to the nearest hundredth.

a.dy

dt

||||t=1

= 3887.56

b.dy

dt

||||t=1

= 647.98

c.dy

dt

||||t=1

= 5831.99

d.dy

dt

||||t=1

= 11663.98

e.dy

dt

||||t=1

= 6479.75

Name: ________________________ ID: A

9

36. Your company is planning to air a number of

television commercials during the ABC television network's presentation of the Academy Awards. ABC is charging your company $560,000 per

30-second spot. Additional fixed costs (development and personnel costs) amount to $700,000, and the network has agreed to provide a

discount of D(x) = 10,000 x for x television

spots. Compute marginal cost C ' (7) and average

cost C (7).

a. C ' (7) = $558,110 per spot; C(7) = $656,120 per sp

b. C ' (7) = $557,110 per spot; C(7) = $656,220 per sp

c. C ' (7) = $558,110 per spot; C(7) = $656,220 per sp

d. C ' (7) = $656,220 per spot; C(7) = $607,165 per sp

e. C ' (7) = $656,220 per spot; C(7) = $558,110 per sp


algebraically.

f (x) = 10 − 3x3

a. f ' (x) = 10 − 9x2

b. f ' (x) = 6x2

c. f ' (x) = -9x2

d. f ' (x) = -9x

e. f ' (x) = 9x2

38. Use a graph to determine whether the function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

g(x) =7x + 2

6x + 2

if x < 0

if x ≥ 0

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

a. The function is continuous on its domain.

b. The points of discontinuity: -2, 0.

c. The point of discontinuity: 2.

d. The points of discontinuity: 2, 0.

e. The point of discontinuity: 0.

39. Calculate dy

dx.

y = x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜ x +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

a.1

xx +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+1

x−

8

x

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜

b.1

2 xx +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+1

2 x+

8

x3

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜

c.x

2x +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+x

2−

8

x3

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜

x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜

d.1

2 xx +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+1

2 x− 8x

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜

e.1

2 xx +

4

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+1

2 x−

8

x3

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x + 4Ê

Ë

ÁÁÁˆ

¯

˜̃˜

Name: ________________________ ID: A

10

40. Use the graph to compute lim

x→0+f (x) and lim

x→0−f (x).

a. lim

x→0+f (x) = 4, lim

x→0−f (x) = 4.

b. lim

x→0+f (x) = 4, lim

x→0−f (x) = −2.

c. lim

x→0+f (x) = −2, lim

x→0−f (x) = −2.

d. + ∞

e. does not exist


limx→+∞

4x4 + 20x

3

718x6 + 1

a. +∞

b. - ∞

c. 0

d.1

718

e. 1

42. Find the slope of the tangent to the graph of the

given function f(x) = 10x + 9 at the indicated point

(-5, -41).

a. f '(-5) = 10

b. f '(-5) = 19

c. f '(-5) = 1

d. f '(-5) = 28

e. f '(-5) = -8

43. Find all points of discontinuity of the function.

g(x) =

x + 5 if x < 0

2x + 5 if 0 ≤ x < 3

x2 + 5 if x ≥ 3

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

a. x = 0, x = 3, x = 5b. x = 0, x = 3c. x = 0d. x = 3e. The function is continuous everywhere.

44. An offshore oil well is leaking oil and creating a

circular oil slick. If the radius of the slick is growing at a rate of 9 miles per hour, find the rate

at which the area is increasing when the radius is 9

miles. (The area of a disc of radius r is A = π r2

.)

a.dA

dt= 9π

mi2

hr

b.dA

dt= 81π

mi2

hr

c.dA

dt= 18π

mi2

hr

d.dA

dt= 27π

mi2

hr

e.dA

dt= 162π

mi2

hr

Name: ________________________ ID: A

11

45. Your monthly profit (in dollars) from selling

magazines is given by P(x) = 8x + 6 x where x is

the number of magazines you sell in a month. If you are currently selling x = 50 magazines per

month, find your profit and your marginal profit.

a. P(50) = $417.32, P'(50) = $0.99

b. P(50) = $442.43, P'(50) = $8.42

c. P(50) = $417.32, P'(50) = $8.42

d. P(50) = $884.85, P'(50) = $8.92

e. P(50) = $221.21, P'(50) = $4.21

46. Calculate dy

dx. You need not expand your answer.

y =x

2.1+

2.1

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

x2 + 2

Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃

a. 2x

b. 2x1

2.1−

2.1

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

c.1

2.1−

2.1

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x2 + 2

Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃ − 2x

x

2.1+

2.1

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

d. 2x1

2.1−

2.1

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

+x

2.1+

2.1

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

x2 + 2

Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃

e.1

2.1−

2.1

x2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜

x2 + 2

Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃ + 2x

x

2.1+

2.1

x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

47. For the slope 0.9, determine at which of the labeled

points on the graph the tangent line has that slope.

a. Q

b. R

c. P

48. Find the value of x for which the marginal profit is zero.

C(x) = 2x, R(x) = 5x −x

2

2,000

a. x = 1,500

b. x = 6,000

c. x = 3,000

d. x = 5,000

e. x = –3,000

Name: ________________________ ID: A

12

49. Use the graph to compute limx→2

f (x) and f (2).

a. limx→2

f (x) = −2 and f (2) = 2

b. limx→2

f (x) = 2 and f (2) = − 2

c. limx→2

f (x) = −2 and f (2) = −2

d. limx→2

f (x) = 2 and f (2) = 2

e. does not exist

50. Find dy

dx using implicit differentiation.

y lnx + y = 2

a. -x

y (lny + 1)

b. -y

x (lnx + 1)

c. -1

x (lnx + 1)

d.y

x lnx

e.y

x (lnx + 1)


limx → 4

x3

− 64

x − 4

a. 48

b. 64

c. 16

d. 17

e. –24

52. The Pentagon is planning to build a new satellite

that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.6 foot/week. Its cost

will be $1,400 per cubic foot. At the point when the

plans call for a satellite 5 feet in radius, how fast is the cost growing? (The volume of a solid sphere of

radius r is V =4

3π r

3.)

a.dP

dt= $60π /week

b.dP

dt= $84,000π /week

c.dP

dt= $1,400,000π /week

d.dP

dt= $42,000π /week

e.dP

dt= $16,800π /week

Name: ________________________ ID: A

13


limx → +∞

3x2 + 4x − 9

10x2

− 10

a.1

11

b.1

10

c.9

10

d.3

10

e. −9

10

54. Calculate dy


y =0.2x

−0.6− 0.9x

−0.7

8.5 + x0.9

a.(-0.12x

-1.6 + 0.63x-1.7)(8.5 + x

0.9) − 0.9x-0.1(0.2x

−0.6− 0.9x

−0.7)

(0.9x-0.1)2

b.(-0.12x

-1.6 + 0.63x-1.7)(8.5 + x

0.9) − 0.9x-0.1(0.2x

0.6− 0.9x

0.7)

8.5 + x0.9

c.(-0.12x

-1.6 + 0.63x-1.7)(8.5 + x

0.9) + 0.9x-0.1(0.2x

0.6− 0.9x

0.7)

(8.5 + x0.9) 2

d.(-0.12x

-1.6 + 0.63x-1.7)(8.5 + x

0.9) − 0.9x-0.1(0.2x

−0.6− 0.9x

−0.7)

(8.5 + x0.9) 2

e.-0.12x

-1.6 + 0.63x-1.7

0.9x-0.1

Name: ________________________ ID: A

14

55. Find dy


xy

12− y

2 = 3

a.1

24xy

b.y

24x − y

c. 24y − 12x

d.y

24y − x

e.1

12y − x

56. Find all the values of x (if any) where the tangent line to the graph of the given equation is horizontal.

y = 19x2 + 3x + 17

a. x = 1.5b. x = -0.08c. x = 0d. x = 0.08e. x = -1.5

57. Find dy


ln(20 + exy

) = y

a.1

20 + exy

(1 − x)

b. x + y

c.ye

xy

20 + exy

d.ye

xy

20 + exy

(1 − x)

e.y

1 − x

58. Find an equation of the tangent line to the graph of

the function f (x) = x +1

x at the point that has

x-coordinate x =1

4.

a. y = 8x − 15

b. y = 15x + 8

c. y = -15x + 8

d. y = x -15

e. y = -15x -120


r (x) = ln 5x + e9x|

||

|||

a.5 + 9e

9x

5x + e9x

b.5 + e

9x

5x + 9e9x

c.5 + e

9x

5x + e9x

d.5 + 9e

9x

5x + 9e9x

e. none of these


limx → 216

x − x3Ê

Ë

ÁÁÁÁ

ˆ

¯

˜̃˜̃

a. 222

b. –6

c. 216

d. 0

e. 210

Name: ________________________ ID: A

15

61. The demand for the Cyberpunk II arcade video

game is modeled by the logistic curve

q(t) =8,000

1 + 0.4e-0.3t

where q(t) is the total number of units sold t months after the game's introduction.

Use technology to estimate q' (6).

Assume that the manufacturers of Cyberpunk II sell

each unit for $1,000. What is the company's

marginal revenue, dR

dq?

Use the chain rule to estimate the rate at which

revenue is growing 6 months after the introduction of the video game.

Please round each answer to the nearest whole number.

a.dq

dt= 140,

dR

dq= 1,000,

dR

dt= 139,614

b.dq

dt= 149,

dR

dq= 1,000,

dR

dt= 148,845

c.dq

dt= 349,

dR

dq= 800,

dR

dt= 349,035

d.dq

dt= 1,163,

dR

dq= 1,000,

dR

dt= 1,163,451

e.dq

dt= 465,

dR

dq= 900,

dR

dt= 465,380

62. Use a graph to determine whether the given

function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

g(x) =3

x2

− 16

a. The points of discontinuity: 1

3,0.

b. The points of discontinuity: 16,0.

c. The point of discontinuity: 0.

d. The function is continuous on its domain.

e. The point of discontinuity: 16.


limx → 2

x − 13

x + 3

a. –2.2

b. 3

c. –0.5

d. 2.2

e. None of these


algebraically.

f (x) =4

x

a. f ' (x) = -4

x

b. f ' (x) = 4

c. f ' (x) = -4

x2

d. f ' (x) = 0

e. f ' (x) =4

x2

Name: ________________________ ID: A

16

65. Find the equation of the straight line, tangent to

y = e5x log2x at the point (1, 0).

a. y (x) =e

2

ln5x +

e2

ln5

b. y (x) =e

5

ln2x +

e5

ln2

c. y (x) =e

5

ln2x −

e5

ln2

d. y (x) =e

2

ln5x −

e2

ln5

e. none of these

66. Calculate the average rate of change of the given function (Inflation (%) of Budget deficit (% of

GNP)) over the interval 0, 2ÈÎÍÍÍ

˘˚˙̇˙ .

a. 16

b. 5.5

c. 3.5

d. –22

e. –1.75


s(x) = 24 x +47

x

a. s'(x) =12

x+

23.5

x x

b. s'(x) =12

x+

23.5

x x

c. s'(x) =12

x−

23.5

x x

d. s'(x) =12

x+

47

x x

e. s'(x) =24

x−

47

x x

68. Find the equation of the line tangent to the graph of

the given function at the point x = 1.

f(x) = (x3 + 2)(x2 + x)

a. y = 6

b. y = 15

c. y = 15x − 9

d. y = 6x

e. y = 15x

Name: ________________________ ID: A

17

69. Use logarithmic differentiation to find dy

dx.

y = (x 3 + x) x3 + 3

a.3x

2 + 1

x3 + x

+3x

2

2x3 + 6

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜

b. 3x2

x3 + 6

3x2 + 1

x3 + x

+x

2

2x3 + 3

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜

c. (x 3 + x) x3 + 3

1

x3 + x

+1

2(x 3 + 3)

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃

d. (3x2 + 1)

3x2 + 1

x+

3x2

2x3 + 6

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜

e. (x 3 + x) x3 + 3

3x2 + 1

x3 + x

+3x

2

2(x 3 + 3)

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜

70. Calculate dy


y =3x + 1

5x − 5

a.3(5x − 5) + 5(3x + 1)

(5x − 5) 2

b. 3(5x − 5) − 5(3x + 1)

c.3(5x − 5) − 5(3x + 1)

(5x − 5) 2

d.3(5x − 5) + 5(3x + 1)

5x − 5

e. 0.6

ID: A

1

MAT 210 TEST 1 REVIEW (Ch 10 and 11)Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1

2. ANS: C PTS: 1

3. ANS: C PTS: 1

4. ANS: E PTS: 1

5. ANS: D PTS: 1

6. ANS: C PTS: 1

7. ANS: E PTS: 1

8. ANS: C PTS: 1

9. ANS: C PTS: 1

10. ANS: C PTS: 1

11. ANS: B PTS: 1

12. ANS: A PTS: 1

13. ANS: E PTS: 1

14. ANS: C PTS: 1

15. ANS: E PTS: 1

16. ANS: D PTS: 1

17. ANS: B PTS: 1

18. ANS: E PTS: 1

19. ANS: E PTS: 1

20. ANS: A PTS: 1

21. ANS: E PTS: 1

22. ANS: E PTS: 1

23. ANS: D PTS: 1

24. ANS: E PTS: 1

25. ANS: D PTS: 1

26. ANS: E PTS: 1

27. ANS: C PTS: 1

28. ANS: E PTS: 1

29. ANS: E PTS: 1

30. ANS: B PTS: 1

31. ANS: C PTS: 1

32. ANS: D PTS: 1

33. ANS: B PTS: 1

34. ANS: C PTS: 1

35. ANS: D PTS: 1

36. ANS: C PTS: 1

37. ANS: C PTS: 1

38. ANS: A PTS: 1

39. ANS: E PTS: 1

ID: A

2

40. ANS: B PTS: 1

41. ANS: C PTS: 1

42. ANS: A PTS: 1

43. ANS: D PTS: 1

44. ANS: E PTS: 1

45. ANS: B PTS: 1

46. ANS: E PTS: 1

47. ANS: A PTS: 1

48. ANS: C PTS: 1

49. ANS: A PTS: 1

50. ANS: B PTS: 1

51. ANS: A PTS: 1

52. ANS: B PTS: 1

53. ANS: D PTS: 1

54. ANS: D PTS: 1

55. ANS: D PTS: 1

56. ANS: B PTS: 1

57. ANS: D PTS: 1

58. ANS: C PTS: 1

59. ANS: A PTS: 1

60. ANS: E PTS: 1

61. ANS: A PTS: 1

62. ANS: D PTS: 1

63. ANS: A PTS: 1

64. ANS: C PTS: 1

65. ANS: C PTS: 1

66. ANS: C PTS: 1

67. ANS: C PTS: 1

68. ANS: C PTS: 1

69. ANS: E PTS: 1

70. ANS: C PTS: 1

mat 210 test 1 review (ch 10 and 11)diane/fall_2012/mat_210/choi... · 2012-10-05 · 1 mat 210...

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