# calculus

F.(0) (10 puntos posibles)

C1   What is limh→0cos(π6+h)−cos(π6)h?

(Enter the answer as a decimal. If the limit does not exist, enter DNE.)

sin responder

C2   At which of the five points on the graph are dydx and d2ydx2 both negative?

Click all that apply.

A
B
C
D
E
- sin responder

C3   What is the average rate of change of the function f(x)=x4−5x between x=0 and x=3?

- sin responder

C4   The position of a particle moving along a line is p(t)=2t3−24t2+90t+7 for t≥0. For what values of t is the speed of the particle increasing?

3<t<4 only
t>4 only
t>5 only
0<t<3 and t>5
3<t<4 and t>5
- sin responder

C5   Evaluate the limit limx→∞ln(x)x2.

0
1
−1

−∞
- sin responder

C6   If f is differentiable at x=a, which of the following must be true?

Choose all of the following that must be true.

f is continuous at x=a.
limx→af(x) exists.
limx→af(x)−f(a)x−a exists.
f′(a) is defined.
f′′(a) is defined.
- sin responder

C7   Let f(x)=x3+5x2−7x−1. What is f′(1)?

- sin responder

C8   Let g(x)=x2ex. What is g′(1)?

(You may enter as decimal number with 2 decimal places, or you can type e for e. Use ∗ to denote multiplication; e.g. 7∗e for 7e.)

sin responder

C9   Suppose that f(x)=g(5x) for all x, and that both functions are differentiable. Which of the following is necessarily true?

f′(1)=g′(1)
f′(5)=g′(1)
f′(1)=g′(5)
5f′(1)=g′(1)
5f′(1)=g′(5)
f′(1)=5g′(1)
f′(1)=5g′(5)
None of the above
- sin responder

C10   Let f(t)=ln(5t+1)t+1−−−−√. What is f′(0)?

f′(0)= - sin responder

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