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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.)
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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
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C3 What is the average rate of change of the function f(x)=x4−5x between x=0 and x=3?
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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
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C5 Evaluate the limit limx→∞ln(x)x2.
0
1
−1
∞
−∞
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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.
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C7 Let f(x)=x3+5x2−7x−1. What is f′(1)?
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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.)
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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
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C10 Let f(t)=ln(5t+1)t+1−−−−√. What is f′(0)?
f′(0)= - sin responder
1 answer