Question 1

Given the graph above, what is $$\lim_{x 	o -5} f(x)$$?

Accepted Answer

$$2$$

Question 2

Given the graph above, what is $$\lim_{x 	o -4} f(x)$$?

Accepted Answer

$$	ext{DNE}$$

Question 3

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

Accepted Answer

$$	ext{DNE}$$

Question 4

Given the graph above, which of the following statements is TRUE?

Accepted Answer

$$f(x) is $$discontinuous at $$x = -5$$

Question 5

Evaluate $$\lim_{x 	o 2} \frac{2x}{x-3}.$$

Accepted Answer

$$-2$$

Question 6

Evaluate $$\lim_{x 	o 5} \frac{x^2$ - 2x - 15}{x^2$ - 25}.$$

Accepted Answer

$$\frac{1}{5}$$

Question 7

For what value of $$c is $$the function $$f(x) = \begin{cases} 2x^2$ + 3 & x \u003c 3 \ cx - 3 & x \geq 3 \end{cases}$$ continuous at $$x = 3$$?

Accepted Answer

$$c = 7.5$$

Question 8

Suppose $$f(5) = 1$$, $$f'(5) = f''(5) = 6$$, $$g(5) = -3$$, and $$g'(5) = 2. $$What is $$(fg)'(5)$$?

Accepted Answer

$$-12$$

Question 9

Find the average rate of change of $$f(x) = 6 + 5x - x^2$ as x$ changes from -2$ to 5$.

Accepted Answer

$$-4$$

Question 10

Find the derivative of $$f(x) = 3x^3$ - 4x^2$ - 5x - 9.$$

Accepted Answer

$$9x^2 - 8x - 5$

Question 11

Find $$f''(x)$$ for $$f(x) = 7x$$^{-3}$$.

Accepted Answer

$$42x^{-5}$$

Question 12

Which of the following best describes the vertical asymptote(s) of $$f(x) = \frac{x^2$ + 3x + 5}{2x - 3}$$?

Accepted Answer

$$x = \frac{3}{2}$$

Question 13

Evaluate $$\lim_{x 	o 0} \frac{\sin(3x)}{\sin(5x) + 3}.$$

Accepted Answer

$$0$$

Question 14

If $$f(x) = x^3$ + 4$$, what is the equation of the tangent line at $$x = 1$$?

Accepted Answer

$$y = 3x + 2$$

Question 15

Find the slant asymptote of $$f(x) = \frac{x^2$ + 3x + 5}{2x - 3}.$$

Accepted Answer

$$y = \frac{1}{2}x + \frac{9}{4}$$

Limits, Continuity, and Graph Analysis in Calculus I

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