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
12. Find the derivative of the function.
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
17. Find the derivative of the function.
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
31. Estimate the limit numerically.
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
¯
˜̃˜̃˜̃
34. Find the derivative of the function.
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
37. Compute the derivative function f '(x)
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
41. Estimate the limit numerically.
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)
51. Calculate the limit algebraically.
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
53. Calculate the limit algebraically.
limx → +∞
3x2 + 4x − 9
10x2
− 10
a.1
11
b.1
10
c.9
10
d.3
10
e. −9
10
54. Calculate dy
dx. You need not expand your answer.
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
dx using implicit differentiation.
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
dx using implicit differentiation.
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
59. Find the derivative of the function.
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
60. Calculate the limit algebraically.
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.
63. Calculate the limit algebraically.
limx → 2
x − 13
x + 3
a. –2.2
b. 3
c. –0.5
d. 2.2
e. None of these
64. Compute the derivative function f '(x)
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
67. Find the derivative of the function.
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
dx. You need not expand your answer.
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
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ID: A
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