If $$\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$$, then $$\lim_{x \to a} f(x)$$ exists.

Question 1

Given the function $$y = -3t^2$ + 8t$$, what is the average velocity over the interval $$[1, 6]$$?

Accepted Answer

$$-13$$

Question 2

For the function $$y = 2x^3$ + 3x^2$ - 5$$, what is the average velocity over the interval $$[2, 5]$$?

Accepted Answer

$$297/3$$

Question 3

Find the average velocity of $$y = 8x^2$ over the interval $$[0, 3/2]$$.

Accepted Answer

$$12$$

Question 4

Evaluate $$\lim_{x 	o 0} f(x)$$ using the first graph provided.

Accepted Answer

$$0$$

Question 5

Using the second graph, what is $$h(4)$$?

Accepted Answer

$$8$$

Question 6

Using the second graph, what is $$\lim_{x 	o 4} h(x)$$?

Accepted Answer

$$6$$

Question 7

Using the second graph, what is $$h(7)$$?

Accepted Answer

Undefined

Question 8

Using the second graph, what is $$\lim_{x 	o 7} h(x)$$?

Accepted Answer

$$1$$

Question 9

Using the third graph, what is $$f(3)$$?

Accepted Answer

$$2$$

Question 10

Using the third graph, what is $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

$$4$$

Question 11

Evaluate $$\lim_{x 	o 2} (x^3$ - 6x^2$ - 5x + 3). $$

Accepted Answer

$$-23$$

Question 12

Evaluate $$\lim_{x 	o 0} (x^3$ - 6x + 8x - 2). $$

Accepted Answer

$$-4$$

Question 13

Evaluate $$\lim_{h 	o 0} \frac{8h}{\sqrt{5h+4} - 2}.$$

Accepted Answer

$$3.2$$

Question 14

Evaluate $$\lim_{x 	o 0} \frac{\sqrt{x+1} - 1}{x}.$$

Accepted Answer

$$\frac{1}{2}$$

Question 15

Suppose a car's position is given by $$s(t) = -3t^2$ + 8t. $$What is the instantaneous velocity at $$t = 1$$?

Accepted Answer

$$2$$

Question 16

Which of the following statements about limits is TRUE?

Accepted Answer

If $$\lim_{x 	o a^-} f(x) = \lim_{x 	o a^+} f(x)$$, then $$\lim_{x 	o a} f(x)$$ exists.

Calculus I Quiz Study Guide: Average Velocity and Limits

Study Guide - Practice Questions