No, because $$g(-2) \neq \lim_{x \to -2} g(x).$$

Question 1

Evaluate the following limit: $$\lim_{x 	o -7} \frac{x^2$ + 7x}{x + 7}.$$

Accepted Answer

Question 2

Given the graph of $$g(x) ($$see image 2), what is $$\lim_{x 	o -2} g(x)$$?

Accepted Answer

$$3$$

Question 3

For the function $$g(x) in $$image 2, is $$g$$ continuous at $$x = -2$$? Why or why not?

Accepted Answer

No, because $$g(-2) 
eq \lim_{x 	o -2} g(x).$$

Question 4

Find the average rate of change of $$f(x) = x^2$ + x - 2x as$$ $$x$$ changes from $$-1 to$$ $$2.$$

Accepted Answer

$$4$$

Question 5

For the function $$f(x) in $$image 3, for which value(s) is $$f'(x)$$ not defined?

Accepted Answer

$$x = 0$$

Question 6

Given $$R(x) = 40x$$ and $$C(x) = 5\sqrt{x} + 100$$, what is the average profit per lamp when $$x$$ lamps are produced and sold?

Accepted Answer

$$40 - \frac{5\sqrt{x} + 100}{x}$$

Question 7

Differentiate $$y = 8\sqrt{x^3$}.$$

Accepted Answer

$$12x\sqrt{x}$$

Question 8

Find the simplified difference quotient for $$g(x) = -3x^2$ + 2.$$

Accepted Answer

$$-6x - 3h$$

Question 9

Find the equation of the tangent line to $$y = x^2$ + 3x at $$the point $$(-1, -2).$$

Accepted Answer

$$y = x - 2$$

Question 10

For $$y = -x^2$ + 8x - 11$$, at which $$x-$$value(s) is the tangent line horizontal?

Accepted Answer

$$x = 4$$

Question 11

Given $$f(x) = x^2$ + 5$$ and $$g(x) = 1 - 2x$$, find $$\frac{d}{dx}(f \circ g)(x).$$

Accepted Answer

$$-4(1 - 2x)$$

Question 12

Evaluate $$\lim_{x 	o 3} (x + 3).$$

Accepted Answer

$$6$$

Question 13

For $$y = x^4$ - 10x^2$ + 13x + 28x$$^{-2}$$, find y$$''$$.

Accepted Answer

$$12x^2 - 20$$ + $$56x^{-4}$$

Question 14

Given the graph of $$g(x) ($$see image 2), what is $$g(-2)$$?

Accepted Answer

$$-2$$

Question 15

For the function $$f(x) in $$image 3, is $$f$$ continuous at $$x = -2$$?

Accepted Answer

Yes, because the graph is unbroken at $$x = -2.$$

Business Calculus Chapter 1 Study Guide – Limits, Continuity, and Derivatives

Study Guide - Practice Questions