# MA16010 Exam 2 Practice Questions Name trolling/16010_E2_Practice.pdf MA16010 Exam 2 Practice Questions A spherical balloon is inﬂated with gas at a rate of 5 cubic centimeters per

Jul 16, 2020

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• MA16010 Exam 2 Practice Questions

Name:

If h(t) = sin(3t) + cos(3t), find h(3)(t).

1.A© 27 sin(3t) + 27 cos(3t)

B© −27 sin(3t)− 27 cos(3t)

C© 27 sin(3t)− 27 cos(3t)

D© −27 sin(3t) + 27 cos(3t)

F© sin(3t) + cos(3t)

A toy rocket is launched from a platform on earth and flies straight up into the air. Its height during the first 10 seconds after launching is given by: s(t) = t3 + 3t2 + 4t + 100, where s is measured in centimeters, and t is in seconds. Find the velocity when the acceleration is 18 cm/s2.

• MA16010 Exam 2 Practice Questions

Find dy

dx by implicit differentiation.

ln(xy) + 2x = ey

= −2− y x− ey

= −2y

1− yey

= −2xy − y x− xyey

= 1 + 2xy

xyey

= −xy − y

2x− xyey

= yey − y x − 2y

Find the critical numbers of y = x2ex.

4.A© −2 and 0

B© 0 and 2

C© 1 and 2

D© 0 and 1

E© −2 and 2

F© -2 and 1

• MA16010 Exam 2 Practice Questions

Given f(x) = 2(3−x2)√

3x2 + 1 . Find f ′(1).

Find the largest open interval where g(t) is increasing.

g(t) = −1 3 t3 +

3

2 t2

F© (−∞, 0) and (3,∞)

• MA16010 Exam 2 Practice Questions

A spherical balloon is inflated with gas at a rate of 5 cubic centimeters per minute. How fast is the radius of the balloon changing at the instant when the radius is 4 centimeters?

The volume V of a sphere with a radius r is V = 4

3 πr3.

centimeters per minute

centimeters per minute

centimeters per minute

centimeters per minute

centimeters per minute

centimeters per minute

Find f ′(2).

f(t) = 2t− 1

(2t+ 1)2

If y = ( 2x−12x+1 ) 3, then dy

dx =

(2x+1)3

(2x+1)4

D© 3( 2x−12x+1 )2

(2x+1)3

• MA16010 Exam 2 Practice Questions

Given f(x) = e5x ln(7x+ e). Find f ′(0).

B© 1 + 7 e

D© 5 + 7 e

F© 1 + 1 e

The price of a commodity is given by p(t) = (t2 + 2t)2 + 100000, where p(t) is the price in dollars and t is years after 2000. At what rate is the price changing in the year of 2010?

Find g′(x) if g(x) = tan2(3x2 + 2).

12.A© 6x tan(3x2 + 2) sec2(3x2 + 2)

B© 12x tan(3x2 + 2) sec2(3x2 + 2)

C© 12x sec2(3x2 + 2)

F© 12x tan(3x2 + 2)

• MA16010 Exam 2 Practice Questions

Use implicit differentiation to find dy dx

if x2 + y2 = 2xy + 5.

13.A© 2x− 2y − 5 2x− 2y

C© 2y − 2x+ 5 2y − 2x

All edges of a cube are expanding at a rate of 2 centimeters per second. How fast is the surface area changing when each edge is 3 centimeters?

Water flows into a right cylindrical shaped swimming pool with a circular base at a rate of 4 m3/min. The radius of the base is 3 m. How fast is the water level rising inside the swimming pool? The volume of a right cylinder with a circular base is V = πr2h, where r is the radius of the base and h is the height of the cylinder.

• MA16010 Exam 2 Practice Questions

A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?

E© − 13 ft/sec

Given f(x) = sin3(2x), find f ′( π12 ).

17.A© − 3 √

3 8

3 4

3 4

Given f(x) = ln 3 √

3 + 3x

3− x , find f ′(1).

• MA16010 Exam 2 Practice Questions

Use implicit differentiation to find the equation of the tangent line to the graph at (−2, 2).

x2 + xy = 4− y2

19.A© y = 2

B© y = −x+ 4

C© y = x+ 2

D© y = x+ 4

E© y = −x+ 2

F© y = −x

Find dy dx

by implicit differentiation.

exy = 8x− 8y

= 8− xexy 8 + yexy

= 8

8 + xexy

= 8 + yexy

8− xexy

= 8

8− xexy

= 8− yexy 8 + xexy

= 8 + xexy

8− yexy

The position of an object moving on a straight line is given by s(t) = 48 − 3t − 2t2 − 6t3, where t is in minutes and s(t) is in meters. What is the acceleration when t = 3 minutes?

• MA16010 Exam 2 Practice Questions

The sides of an equilateral triangle are expanding at a rate of 2 cm per minute. Find the rate of change of the area

when the length of each side is 3 cm. Use the fact that the area of an equilateral triangle is A = √

3 4 x

2 , where x is the length of a side.

3 4 cm

2/min

3 cm2/min

3 2 cm

2/min

3 4 cm

2/min

3 cm2/min

3 2 cm

2/min

Given f(x) = x3

3 + x+

√ x3. Find f ′′(4).

Given y = x ln x, find y′′(e).

+ 1

• MA16010 Exam 2 Practice Questions

Find the relative extrema of g(x) = x

x2 + 9 .

25.A© Relative maximum at x = √

3; Relative minimum at x = − √

3

B© Relative maximum at x = 3; Relative minimum at x = −3

C© Relative maximum at x = 3; Relative minimum at x = − √

3

D© Relative maximum at x = − √

3; Relative minimum at x = √

3

E© Relative maximum at x = −3; Relative minimum at x = √

3

F© Relative maximum at x = −3; Relative minimum at x = 3

Find the largest open interval(s) on which f(x) = (3x− 4)(x+ 2)

is increasing.

26.A© (− 13 ,∞)

C© (−∞, 3) and (3,∞)

D© (−∞,− 13 )

E© (−∞,−2) and (43 ,∞)

F© (−2, 43 )

If x and y are both functions of t and x+ y2 = 4ex,

find dy dt

when dx dt

= 2, x = 0, and y = −2.

• MA16010 Exam 2 Practice Questions

Find g′(1).

g(x) =

(

x2

x+ 2

)3

The position of a particle on a straight line t seconds after it starts moving is s(t) = 2t3 − 3t2 + 6t+ 1 feet. Find the acceleration of the particle when its velocity is 78 ft/sec.

Find the relative maximum of f(x) = 2x3 − 6x.

• MA16010 Exam 2 Practice Questions

Given that y2x− x2 = y ln(x) + 3,

use implicit differentiation to find dydx at (1,−2).

Find f ′(4) if f(x) = (x2 + 3) √ x2 − 7.

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