$$\lim_{x \to -2^-} f(x) = -2$$, $$\lim_{x \to -2^+} f(x) = -7$$

$$\lim_{x \to 2^-} f(x) = 4$$, $$\lim_{x \to 2^+} f(x) = -3$$

Question 1

Given the function $$y = x^2$ + 9x$$, what is the average velocity over the interval $$[2, 7]$$?

Accepted Answer

$$18$$

Question 2

For the function $$y = 3x - 2$$, what is the average velocity over the interval $$[5, 8]$$?

Accepted Answer

$$-16$$

Question 3

Find the average velocity of $$y = -3x^2$ - x$$ over the interval $$[3, 4].$$

Accepted Answer

$$-22$$

Question 4

Evaluate $$\lim_{x 	o 0} f(x)$$ using the graph in Image 1.

Accepted Answer

The limit does not exist

Question 5

Evaluate $$\lim_{x 	o 0} f(x)$$ using the graph in Image 2.

Accepted Answer

The limit does not exist because the function is undefined at $$x=\pm\sqrt{7}$$

Question 6

Evaluate $$\lim_{x 	o -2^-} f(x)$$ and $$\lim_{x 	o -2^+} f(x)$$ using the graph in Image 3.

Accepted Answer

$$\lim_{x 	o -2^-} f(x) = -2$$, $$\lim_{x 	o -2^+} f(x) = -7$$

Question 7

Evaluate $$\lim_{x 	o 2^-} f(x)$$ and $$\lim_{x 	o 2^+} f(x)$$ using the graph in Image 4.

Accepted Answer

$$\lim_{x 	o 2^-} f(x) = 4$$, $$\lim_{x 	o 2^+} f(x) = -3$$

Question 8

Evaluate $$\lim_{x 	o 1^+} f(x)$$ using the graph in Image 5.

Accepted Answer

$$3$$

Question 9

Find all vertical asymptotes of the function $$f(x) = \frac{x-8}{x^2$-9}.$$

Accepted Answer

$$x = -3, 3$$

Question 10

Find all horizontal asymptotes of the function $$f(x) = \frac{8x+1}{x^2$-25}.$$

Accepted Answer

$$y = 0$$

Question 11

For the function $$y = x + 2$$, over which intervals is the function continuous?

Accepted Answer

$$(-\infty, \infty)$$

Question 12

For the function $$y = 5\cos(	heta)/(	heta + 3)$$, at which value is the function discontinuous?

Accepted Answer

$$	heta = -3$$

Question 13

Evaluate $$\lim_{x 	o 0} \frac{\sqrt{x+9} - 3}{x}.$$

Accepted Answer

$$\frac{1}{6}$$

Question 14

Evaluate $$\lim_{x 	o \infty} \frac{7x+3}{5x^2$+1}.$$

Accepted Answer

$$0$$

Question 15

A car's position is given by $$s(t) = 2 + 	an t. $$What is the average velocity over $$[-\frac{\pi}{4}, \frac{\pi}{4}]$$?

Accepted Answer

$$\frac{4}{\pi}$$

Question 16

Evaluate $$\lim_{x 	o 0} \frac{x^3$ - 9x + 18}{x - 6}.$$

Accepted Answer

$$-3$$

Question 17

Find the intervals on which the function $$y = \frac{x+2}{x^2$-15x+56} is $$continuous.

Accepted Answer

$$(-\infty, 7) \cup (7, 8) \cup (8, \infty)$$

Calculus Study Guide: Average Velocity, Limits, Asymptotes, and Continuity

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