Calc Test

The graph of the function f is shown above. Of the following intervals, on which is f continuous but not differentiable?

(2,3)

The figure above shows the graphs of the functions f and g. If h(x) = f(x)g(x), then h'(2) =

-11/2

If f is the function given by f(x) = 3x^2-x^3 then the average rate of change off on the closed interval [1, 5 ] is

-13

The function f is continuous and increasing for x >_ -1. The table above gives values of f at selected values of x. Of the following, which is the best approximation for lim x-> 0 of e^-2f(x)

1

Let f be the function defined above, where k is a positive constant. For what value of k, if any, is f continuous?

2.081

For time t >_ 1, the position of a particle moving along the x-axis if given by p(t) = sqrt t - 2. At what time t in the interval 1<_ t <_ 16 is the instantaneous velocity of the particle equal to the average velocity of the particle over the interval 1<_ t <_ 16

25/4

The table above shows selected values of a continuous function f For 0 x 13, what is the fewest possible number of times f(x) = 4 ?

3

The function f is differentiable and has values as shown in the table above. Both f and f' are strictly increasing on the interval 0 <_ x <_5. Which of the following could be the value of f' (3)?

30

the table above gives values of the differentiable functions f and g and their derivatives at x= 1. If h(x) = (2f(x)+3)(1 + g(x)), then h'(1) =

44

The function f is given by f(x) = sin(x+1/x^2). Which of the following is true

I only( horizontal asymptote at y=0

The function h is defined on the closed interval [−1, 3]. The graph of h', the derivative of h, is shown above. The graph consists of two semicircles with a common endpoint at x = 1. Which of the following statements about h must be true?

II only

Let f be the function given by f(x) = x-2/2|x-2|. Which of the following is true

f has a jump discontinuity at x = 2

Let f be a function such that f (1) = — 2 and f (5) = 7. Which of the following conditions ensures that f(c) = 0 for some value c in the open interval (1,5)?

f is continuous on the closed interval [1,5]

Let f be a function such that f(1) = -2 and f(5) = 7 . Which of the following conditions ensures that f(c) = 0 for some value c in the open interval f of c, equals 0?

f is continuous on the closed interval [1,5]

Let f be a differentiable function. The figure above shows the graph of the line tangent to the graph of f at x = 0. Of the following, which must be true?

f'(0)=f(0)

The figure above shows the graph of a function f. Which of the following has the greatest value?

f'(a)

The function f is not differentiable at = 5. Which of the following statements must be true?

lim x ->5 of f(x)-f(5)/x-5 DNE

If f is a differentiable function such that f(3)=8 and f' (3) = 5, which of the following statements could be false?

lim x->3 f'(x)=5

For values of h very close to 0, which of the following functions best approximates f(x) = tan(x+h)-tan(x)/h

sec^2 x

Which of the following is an equation of the line tangent to the graph of y = cos at x = pi/2

y = -x+pi/2

The graph of which of the following functions has exactly one horizontal asymptote and no vertical asymptotes?

y = 1/x^2 +1

The continuous function f is positive and has domain x > 0. If the asymptotes of the graph of f are x = 0 and y which of the following statements must be true?

Limit as x approaches 0 from the right is infinity and limit as x approaches infinity is 2

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.