Question 1

Calculate the average rate of change of $$f(x) = x^2$ - 4x + 7$$ over the interval $$[1, 3].$$

Accepted Answer

$$-3$$

Question 2

Find the average rate of change of $$f(x) = \sin(x)$$ over the interval $$[0, \frac{\pi}{6}].$$

Accepted Answer

Question 3

A rock is launched vertically upward from the ground with a speed of $$85 ft/sec. $$Its position after $$t$$ seconds is $$s(t) = -16t^2$ + 85t. $$What is the average rate of change of the rock's position between $$1$$ and $$3$$ seconds?

Accepted Answer

$$-31 ft/sec$$

Question 4

Evaluate $$\lim_{x 	o 2} f(x)$$ using the first graph (piecewise function with a jump at $$x=2).$$

Accepted Answer

$$-1$$

Question 5

For the second graph, what is $$f(1)$$?

Accepted Answer

$$	ext{undefined}$$

Question 6

For the second graph, what is $$\lim_{x 	o 1^-} f(x)$$?

Accepted Answer

$$1$$

Question 7

For the second graph, what is $$\lim_{x 	o 1^+} f(x)$$?

Accepted Answer

$$	ext{DNE}$$

Question 8

For the third graph, what is $$f(-4)$$?

Accepted Answer

$$2$$

Question 9

For the third graph, what is $$\lim_{x 	o -4^-} f(x)$$?

Accepted Answer

$$3$$

Question 10

For the third graph, what is $$\lim_{x 	o -4^+} f(x)$$?

Accepted Answer

$$2$$

Question 11

For the third graph, does $$\lim_{x 	o -4} f(x)$$ exist?

Accepted Answer

$$	ext{DNE}$$

Question 12

Which of the following statements is true about two-sided limits?

Accepted Answer

A two-sided limit exists if and only if both one-sided limits exist and are equal.

Question 13

Suppose $$f(x) is $$defined as $$f(x) = e^x. $$What is the average rate of change of $$f(x)$$ over $$[0, \ln(3)]$$?

Accepted Answer

$$2$$

Question 14

For the first graph, what is $$\lim_{x 	o 2^-} f(x)$$?

Accepted Answer

$$1$$

Question 15

For the first graph, what is $$\lim_{x 	o 2^+} f(x)$$?

Accepted Answer

$$-1$$

Question 16

For the first graph, what is $$f(2)$$?

Accepted Answer

$$2$$

Question 17

For the third graph, what is $$\lim_{x 	o 4} f(x)$$?

Accepted Answer

$$	ext{DNE}$$

Question 18

For the third graph, what is $$f(4)$$?

Accepted Answer

$$-3$$

Question 19

For the third graph, what is $$\lim_{x 	o 4^-} f(x)$$?

Accepted Answer

$$-2$$

Question 20

For the third graph, what is $$\lim_{x 	o 4^+} f(x)$$?

Accepted Answer

$$-3$$

Guided Study: Limits and Average Rate of Change (Calculus I)

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