Calc AB MC questions

The table above gives selected values for the differentiable function f. In which of the following intervals must there be a number c such that f′(c)=2 ? A. (0,4) B. (4,8) C. (8,12) D. (12,16)

(8,12)

∫1 −1 x^2−x/xⅆx A. -2 B. 0 C. 4/3 D. Nonexistent

-2

The graph of the piecewise linear function ff is shown above. What is the value of ∫12 f′(x)ⅆx 0 A. -8 B. -6 C. 0 D.22

-8

The graph of a function f is shown above. If g is the function defined by g(x)=(x^2+1)/f(x), what is the value of g′(2) ? A. -8/9 B. 1/9 C. 1 D. 32/9

-8/9

lim (sinx)/e^x −1 x→0 A. 1 B. 1/e C. 0 D. Nonexistent

1

The base of a solid is the region in the first quadrant bounded by the y-axis, the x-axis, the graph of y=e^x, 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? A. E-1 B. 1/2e^2−1/2 C. E^2-1 D.2e^-2

1/2e^2−1/2

What is the value of x at which the minimum value of y=3x^4/3−2x occurs on the closed interval [0,1] ? A. 0 B. 1/8 C. 1/2h D. 1

1/8

For any real number x, lim (sin(2(x+h))−sin(2x))/h= h→0 A. 0 B. 1 C. Cos(2x) D.2cos(2x)

2 cos(2x)

A particle moves along a straight line so that at time t≥0 its acceleration is given by a(t)=12t. At time t=0, the velocity of the particle is 2 and the position of the particle is 5. Which of the following is an expression for the position of the particle at time t≥0 ? A. 6t^2+5 B. 6t^3+2t+5 C.2t^3+5 D. 2t^3+2t+5

2t^3+2t+5

d/dx(x^3 sec(2x))= A. 6x^2sec(2x)tan(2x) B. 2x^3tan^2(2x)+3x^2sec(2x) C. X^3sec(2x)tan(2x)+3x^2sec(2x) D.2x^3sec(2x)tan(2x)+3x^2sec(2x)

2x^3sec(2x)tan(2x)+3x^2sec(2x)

If ⅆy/ⅆx=2−y and if y=1 when x=1, then y= A. 2-e^x-1 B. 2-e^1-x C. 2-e^-x D. 2+e^-x

2−e^1−x

A person stands 30 feet from point P and watches a balloon rise vertically from the point, as shown in the figure above. The balloon is rising at a constant rate of 2 feet per second. What is the rate of change, in radians per second, of angle θ at the instant when the balloon is 40 feet above point P ? A. 3/100 B. 3/125 C.1/12 D. 5/27

3/125

Let gg be the function given by g(x)=∫x (t2−5t−14)ⅆt. 3 What is the x-coordinate of the point of inflection of the graph of g? A. -2 B. 5/2 C.3 D.7

5/2

lim (10−6x^2)/(5+3e^x) is x→∞ A. -2 B. 0 C. 2 D. Nonexistent

B

∫(x^2/4)ⅆx= A. Pi/2+C B. (x^3/12)+C C.x^3/4+C D. 3X^4+C

B

Let R be the region bounded by the graphs of y=2x and y=4x−x^2. What is the area of R? A. 2/3 B.4/3 C. 16/3 D. 28/3

B.4/3

The function f is given by f(x)=4x^3−x^4. On what intervals is the graph of f concave up? A. (-infinity, 0) B. (-Infinity, 3) C. (0,2) only D. (0,3) only

C

Which of the following is an equation of the line tangent to the graph of y=cosx at x=π/2 ? A. y=−x+π/2. B. Y=x-pi/2 C. Y=-x+pi/2 D.Y=-x-pi/2

C

If x+3y^1/3=y what is ⅆy/ⅆx at the point (2,8) ? A. 1/3 B. 3/4 C. 5/4 D. 4/3

D

d/dx(2(sin√x)^2)= A. 4cos(1/2√x) B. 4sin√x cos√x C. 2sin√x/√x D. (2sin√xcos√x)/√x

D

ⅆ/ⅆx(x^5−5x)= A. X^6/6-5^x/ln5 B. 5x^4-5^x C. 5x^4-x⋅5^x-1 D. 5x^4−(ln5)5^x

D

∫(x^2+1)/(x3+3x−5)^3ⅆx= A. -3/2⋅1/(3x^2+3)^2+C B. −1/6⋅1/(3x^2+3)^2+C C. -3/2⋅1/(x^3+3x-5)^2+C D. −1/6⋅1/(x^3+3x-5)^2+C

D

A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t^3−4t^2+4t+3. Which of the following statements describes the motion of the particle at time t=1?

The particle is moving down the y-axis with decreasing velocity

At time t=0, a storage tank is empty and begins filling with water. For t>0 hours, the depth of the water in the tank is increasing at a rate of W(t) feet per hour. Which of the following is the best interpretation of the statement W′(2)>3 ? A. Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than feet per hour. B.Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than feet per hour per hour.

Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.

The function f is continuous on the closed interval [0,5]. The graph of f′, the derivative of f, is shown above. On which of the following intervals is f increasing? A. [0,1] and [2,4] B. [0,1] and [3,5] C. [0,1] and [4,5] only D. [0,2] and [4,5]

[0,2] and [4,5]

For what value of bb does the integral ∫b x2ⅆx 1 n equal lim ∑ (1+2k/n)^2 2/n n→∞ k=1 A. B=2 only B. B=3only C. B could be any real number D. There is no such value do b

b=3 only

Shown above is a slope field for which of the following differential equations? A. Dy/dx= |x+y| B.Dy/dx=x^3 C.Dy/dx=y^3 D.Dy/dx=y^2

dy/dx=y^2

f(x)={−x^2+3. if x≤5 −10x+28 if x>5

f is continuous and differentiable at x=5

How many vertical asymptotes does the graph of y=(x−2)/(x^4−16) have? A. 1 B. 2 C. 3 D. 4

one

The equation y=2e6x−5 is a particular solution to which of the following differential equations?

y′−6y−30=0

If ∫4 f(x)ⅆx=8 and 1 ∫1 4g(x)ⅆx=−2, which of the following cannot be determined from the information given?

∫4 3f(x)g(x)ⅆx 1