Calc AB MC questions

d/dx(2(sin√x)^2)=

(2sin√xcos√x)/x

For any real number x, lim (sin(2(x+h))−sin(2x))/h= h→0

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 ?

2t^3+2t+5

d/dx(x^3 sec(2x))=

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

If ⅆy/ⅆx=2−y and if y=1 when x=1, then y=

2−e^1−x

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

y′−6y−30=0

∫(x^2+1)/(x3+3x−5)^3ⅆx=

−1/6⋅1/(x^3+3x−5)^2+C

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

The function f is given by f(x)=4x^3−x^4. On what intervals is the graph of f concave up?

(0,2) only

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 ?

(8,12)

∫(x^2/4)ⅆx=

(x^3/12)+C

What is the value of ∫13 f(x)ⅆx 0

-2

∫1 −1 x^2−x/xⅆx

-2

The graph of the piecewise linear function ff is shown above. What is the value of ∫12 f′(x)ⅆx 0

-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) ?

-8/9

lim (10−6x^2)/(5+3e^x) is x→∞

0

lim (sinx)/e^x −1 x→0

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?

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] ?

1/8

Let gg be a twice-differentiable function with g′(x)>0 and g′′(x)>0 for all real numbers x, such that g(3)=12 and g(5)=18 Which of 20, 21, and 22 are possible values for g(6) ?

22 only

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 ?

3/125

If x+3y^1/3=y what is ⅆy/ⅆx at the point (2,8) ?

4/3

Let RR be the region bounded by the graphs of y=2x and y=4x−x^2. What is the area of RR ?

4/3

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?

5/2

ⅆ/ⅆx(x^5−5x)=

5x^4−(ln5)5^x

If f is a function that has a removable discontinuity at x=3, which of the following could be the graph of f ?

the linear one

The table above gives values of the differentiable function f and its derivative at selected values of x. If g is the inverse function of f, which of the following is an equation of the line tangent to the graph of g at the point where x=2 ?

y=1/5(x−2)+3

Which of the following is an equation of the line tangent to the graph of y=cosx at x=π/2 ?

y=−x+π/2.

For what value of bb does the integral ∫b x2ⅆx 1 n equal lim ∑ (1+2k/n)^2 2/n n→∞ k=1

b=3 only

Shown above is a slope field for which of the following differential equations?

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

The graph of y=f(x) on the interval 0<x<5 is shown above. Which of the following could be the graph of y=f′(x)?

flat then positive

How many vertical asymptotes does the graph of y=(x−2)/(x^4−16) have?

one

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 ?

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?

[0,2] and [4,5]