Question 1

Given the graph of $$f(x) in $$Image 1, what is $$\lim_{x 	o 0^-} f(x)$$?

Accepted Answer

$$4$$

Question 2

Given the graph of $$f(x) in $$Image 1, what is $$\lim_{x 	o 0^+} f(x)$$?

Accepted Answer

$$2$$

Question 3

Given the graph of $$f(x) in $$Image 1, what is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$d.n.e.$$

Question 4

Given the graph of $$f(x) in $$Image 2, what is $$\lim_{x 	o 0^-} f(x)$$?

Accepted Answer

$$2$$

Question 5

Given the graph of $$f(x) in $$Image 2, what is $$\lim_{x 	o 0^+} f(x)$$?

Accepted Answer

$$4$$

Question 6

Given the graph of $$f(x) in $$Image 2, what is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$d.n.e.$$

Question 7

According to the Mean Value Theorem, which of the following must be true for a function $$f on$$ $$[a, b]$$?

Accepted Answer

There exists $$c in$$ $$(a, b)$$ such that $$f'(c) = \frac{f(b) - f(a)}{b - a}$$

Question 8

For $$f(x) = x^2$ + 3x - 4 on$$ $$[0, 2]$$, what value of $$c$$ satisfies the Mean Value Theorem?

Accepted Answer

$$c = \frac{2}{\sqrt{3}}$$

Question 9

A farmer plans to make four identical and adjacent rectangular pens against a barn, each with 80 square feet area. What are the dimensions of each pen that minimize the amount of fence used?

Accepted Answer

$$x = 50, y = 100$$

Question 10

For the function $$f(x) = 2x^3$ - 5x^2$ + 7 on$$ $$[-1, 3]$$, what is the absolute maximum?

Accepted Answer

At $$x = 2$$

Question 11

For the function $$f(x) = x^2$ + 2x on$$ $$[0, \infty)$$, what is the absolute minimum?

Accepted Answer

At $$x = 0$$

Question 12

For the function $$f(x) = x^2$ on $$[0, \infty)$$, what is the absolute minimum?

Accepted Answer

At $$x = 0$$

Question 13

For the function $$f(x) = x^2$ + 2x on$$ $$[0, \infty)$$, what is the absolute maximum?

Accepted Answer

No absolute maximum

Question 14

For the function $$f(x) = x^2$ on $$[0, \infty)$$, what is the absolute maximum?

Accepted Answer

No absolute maximum

Limits and Continuity: Analyzing Limits from Graphs

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