Packet 1 Ap calc

C) 1.633

76) A particle moves along the x-axis so that at any time t>0 , its velocity is given by v(t)=3+4.1cos(0.9t). what is the acceleration of the particle at t=4

C) 4

77) The regions A, B, and C in the figure above are bounded by the graph of the functions and the x-axis. If the area of each region is 2, what is the value of the integration from -3 to 3 (f(x) +1)dx?

C) 4pi m^2/sec

78) The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumerence of teh circle is 20pi meters?

D) I and II only

79) For which of the following does lim x approaching 4 f(x) exist?

B) There exists c, where -2<c<1, such that f'(c)=0

80) The function f is continuous for -2<x<1 and differentiable for -2<x<1. If f(-2)= -5 and f(1)=4, which of the following statements could be false?

D) four

81) Let f be function with derivatives given by f'(x)=sin(x^2 +1). How many relative extrema does f have on the interval 2<x<4

A) integration from 1.572 to 3.514 of r(t) dt

82) The rate of change of the altitude of a hot-air balloon is given by r(t)= t^3 -4t^2 +6 for )<t<8. Which of the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing

A) 20.086 ft/sec

83) The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t)=e^t + te^t. What is the average velocity of the particle from time t=0 to time t=3

A) 112F

84) A pizza heated to temp of 350 degrees F, is taken out of an oven and placed in a 75F room at time t=0 minutes. The temp of the pizza is changing at a rate of -110e^-0.04t degrees F per minute. To the nearest degree, what is the temp of the pizza at time t=5

A

85) If a trapezoidal sum overapproximates integration from 0 to 4 f(x) dx, and a right Riemann sum underapproximtes it, which of the following could be the graph of y=f(x)

D) 8.755

86) the base of a solid is the region in the first quadrant bounded by the y-axis, the graph of y=tan^-1(x), the horizontal line y=3, and the vertical line x=1. For this solid, each cross section perpendicular to the x-axis is a square. what is the volume of the solid

D) -0.278

87) The function f has first derivative given by f'(x)= (x^1/2)/(1+x+x^3). Which is the x-coordinate of the inflection point of the graph of f

C

88) on the closed interval (2,4), which of the following could be the graph of a function f with the property that 1/4-2 integration from 2 to 4 of f(t)dt=1

D) y-6=-7(x-2)

89) Let f be a differentiable function with f(2)=3 and f'(2)=-5, and let g be the function defined by g(x)=xf(x). which of the following is an equation of the line tangent to to the graph of g at the point where x=2

B

90) For all x in the closed interval (2,%), the function f has a positive first derivative and a negative second derivative. which of the following could be a table of values for f?

E) 3.346

91) a particle moves along the x-axis so that at any time t>0, its acceleration is given by a(t)= ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is

D) 1.772< x < 2.507

92) let g be the function given by g(x)=integration from 0 to x of sin(t^2)dt for -1<t<3. On which of the following intervals is g decreasing?

D) y=x^2+ 3x-2

A curve has slope 2x+3 at each point (x,y) on the curve. Which of the following is an equation for this curve if it passes through the point (1,2)

E) t=3 and t=4

A particle moves along the x-axis so that at time t>0 its position is given by x(t)= 2t^3-21t^2+72T-53. At what time t is the particle at rest

C) 3

If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2,2), then f'(1) is

E) 6x^2(x^3=1)

If y=(x^3+1)^2, then dy/dx=

D) -5/(3x+2)^2

If y=2x+3/3x+2, then dy/dx=

E) 2x(sin 2x+x cos 2x)

If y=x^2sin2x, then dy/dx=

D) 1/4 - e^-4/4

Integration from 0 to 4 of e^-4x dx=

B) /4

Let f be the function defined by f(x)= x^3+x. If g(x)=f^-1(x) and g(2)=1, what is the value of g'(2)?

C) y=7x+11

Let f be the function defined by f(x)=4x^3-5x=3. Which of the following is an equation of the line tangent to the graph of f at the point where x=-1

A) x< -2

Let f be the function given by f(x)=2xe^x. The graph of f is concave down when

D) (0, 2^1/3)

Let f be the function with derivative given by f'(x)= x^2- 2/x. On which of the following intervals is f decreasing?

E) 27

Let g be a twice differentiable function with g'(x)>0 and g"(x)>0 for all real numbers x, such that g(4)=12 and g(5)=18. of the following, which is possible value for g(6)

B) 4/9

What is the slope of the line tangent to the curve 3y^2-2x^2= 6-2xy at the point (3,2)

E) 2xsin(x^6)

d/dx( integration from 0 to x^2 of sin (t^3) dt)

D) I and II only

f(x)= x+2 if x<3 =4x-7 if x>3 Let f be the function given above. whih of the followng statements is true about f?

D) -2^1/2/2 + 1

integration from 0 to pi/4 sin x dx=

B) 1/3sin(x^3)+C

integration of x^2cos(x^3) dx

C) 1/4

lim x to infinity x^3-2x^2+3x-4/ 4x^3-3x^2+2x-1

A) 0 and a only

the second derivative of the function f is given by f''(x)=x(x-a)(x-b)^2. The graph of f" is shown above. For what values of x does the graph of f have a point of inflection

C) 1/2 integration from 1 to 5 u^1/2 du

using the substitution u=2x=1, integration from 0 to 2 of (2x+1)^1/2 dx is equivalent to

A) -2/5

If f(x)=ln(x+4+e^-3x), then f1(0) is

E) lim x to infinity f(x)=2

For X>0, the horizontal line y=2 is an asymptote for the graph of the function f. which of the following statements must be true?

A) -2<x<2 only

The derivative g' of a function g is continuous and has exactly two zeros. Selected g values of g' are given in the table above. If the domain of g is the set of all real numbers, then g is decreasing on which of the following intervals?

B

The function f has the property that f(x), f1(x), and f2(x) are negative for all real values x. Which of the following could be the graph of f

A) a

The graph of a function f is shown above. At which value of x is f continuous, but not differentiable?

D) 8

The graph of f', the derivative of f, is the line shown in the figure above. If f(0)=5, then f(1)=

B) f is increasing for -2<x<0

The graph of f1, the derivative of the function f, is shown above. which of the following statements is true about f?

E) dV/dt= k(V)^1/2

The rate of change of the volume V, of water in a tank with respect to time,t, is directly propotional to the square root of the volume. Which of the following is a differential equation that describes this relationship?