Top Banner

Click here to load reader

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

ReportDownload

Documents

others

  • 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)

    E© sin(3t)− 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.

    2.A© 44 cm/s

    B© 2 cm/s

    C© 28 cm/s

    D© 16 cm/s

    E© 32 cm/s

    F© 13 cm/s

  • MA16010 Exam 2 Practice Questions

    Find dy

    dx by implicit differentiation.

    ln(xy) + 2x = ey

    3.A© dy dx

    = −2− y x− ey

    B© dy dx

    = −2y

    1− yey

    C© dy dx

    = −2xy − y x− xyey

    D© dy dx

    = 1 + 2xy

    xyey

    E© dy dx

    = −xy − y

    2x− xyey

    F© dy dx

    = 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).

    5.A© −7 2

    B© −1 2

    C© −13 6

    D© −3 2

    E© −9 4

    F© −3 4

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

    g(t) = −1 3 t3 +

    3

    2 t2

    6.A© (−∞, 0)

    B© (0,∞)

    C© (−∞, 3)

    D© (0, 3)

    E© (3,∞)

    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.

    7.A© 5π 64

    centimeters per minute

    B© 5 4π

    centimeters per minute

    C© 5 16π

    centimeters per minute

    D© 5 64π

    centimeters per minute

    E© 256π 3

    centimeters per minute

    F© 25 4π

    centimeters per minute

    Find f ′(2).

    f(t) = 2t− 1

    (2t+ 1)2

    8.A© 22125

    B© − 2125

    C© − 110

    D© 2125

    E© − 225

    F© 4124

    If y = ( 2x−12x+1 ) 3, then dy

    dx =

    9.A© 12(2x−1) 2

    (2x+1)3

    B© 48 (2x+1)4

    C© 12(2x−1) 2

    (2x+1)4

    D© 3( 2x−12x+1 )2

    E© 24x−12(2x+1)3

    F© 6(2x−1) 2

    (2x+1)3

  • MA16010 Exam 2 Practice Questions

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

    10.A© 35 e

    B© 1 + 7 e

    C© 1 e

    D© 5 + 7 e

    E© 5 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?

    11.A© $5280/year

    B© $900/year

    C© $2640/year

    D© $4800/year

    E© $2400/year

    F© $1680/year

    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)

    D© 2 sec2(6x)

    E© 2 tan(6x)

    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

    B© x x−y

    C© 2y − 2x+ 5 2y − 2x

    D© 1

    E© 0

    F© x 1−y

    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?

    14.A© 36 cm2/sec

    B© 12 cm2/sec

    C© 72 cm2/sec

    D© 48 cm2/sec

    E© 54 cm2/sec

    F© 46 cm2/sec

    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.

    15.A© 29π m/min

    B© 49π m/min

    C© 23π m/min

    D© 43π m/min

    E© 316π m/min

    F© 38π m/min

  • 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?

    16.A© 14 ft/sec

    B© 8 ft/sec

    C© 4 ft/sec

    D© −3 ft/sec

    E© − 13 ft/sec

    F© −34 ft/sec

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

    17.A© − 3 √

    3 8

    B© 12

    C© − √

    3 4

    D© 3 √

    3 4

    E© 32

    F© 94

    Given f(x) = ln 3 √

    3 + 3x

    3− x , find f ′(1).

    18.A© 13

    B© 23

    C© 12

    D© 16

    E© 14

    F© 18

  • 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

    20.A© dy dx

    = 8− xexy 8 + yexy

    B© dy dx

    = 8

    8 + xexy

    C© dy dx

    = 8 + yexy

    8− xexy

    D© dy dx

    = 8

    8− xexy

    E© dy dx

    = 8− yexy 8 + xexy

    F© dy dx

    = 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?

    21.A© -177 m/min2

    B© -114 m/min2

    C© -110 m/min2

    D© -112 m/min2

    E© -108 m/min2

    F© -76 m/min2

  • 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.

    22.A© 9 √

    3 4 cm

    2/min

    B© √

    3 cm2/min

    C© 3 √

    3 2 cm

    2/min

    D© 3 √

    3 4 cm

    2/min

    E© 3 √

    3 cm2/min

    F© 9 √

    3 2 cm

    2/min

    Given f(x) = x3

    3 + x+

    √ x3. Find f ′′(4).

    23.A© 496

    B© 498

    C© 192

    D© 678

    E© 354

    F© 263

    Given y = x ln x, find y′′(e).

    24.A© 0

    B© 1 e

    C© 2

    D© 1 e

    + 1

    E© e+ 1

    F© e

  • 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 ,∞)

    B© (−∞, 3)

    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.

    27.A© 1

    B© − 32

    C© 0

    D© −1

    E© − 12

    F© 3

  • MA16010 Exam 2 Practice Questions

    Find g′(1).

    g(x) =

    (

    x2

    x+ 2

    )3

    28.A© 13

    B© 527

    C© 53

    D© 2527

    E© 59

    F© 253

    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.

    29.A© 46 ft/sec2

    B© 30 ft/sec2

    C© 84 ft/sec2

    D© 42 ft/sec2

    E© 105 ft/sec2

    F© 258 ft/sec2

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

    30.A© (−1, 0)

    B© (1,−4)

    C© (1, 4)

    D© (1, 0)

    E© (0, 0)

    F© (−1, 4)

  • MA16010 Exam 2 Practice Questions

    Given that y2x− x2 = y ln(x) + 3,

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

    31.A© − 25

    B© 5

    C© 1

    D© −2

    E© 2

    F© −1

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

    32.A© 1103

    B© 1636

    C© 323

    D© 1483

Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.