Q: Which of the following statements is true about $$\displaystyle \lim_{x \to 3} f(x)$$?

$$\displaystyle \lim_{x \to 3} f(x) = 2$$

Q: If a two-sided limit exists at $$x = a$$, which of the following must be true?

$$\displaystyle \lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$$

Question 1

Given the graph of $$y = f(x)$$, what is $$\displaystyle \lim_{x 	o 2} f(x)$$?

Accepted Answer

$$2$$

Question 2

Based on the graph, what is the value of $$f(2)$$?

Accepted Answer

$$3$$

Question 3

Which of the following statements is true about $$\displaystyle \lim_{x 	o 3} f(x)$$?

Accepted Answer

$$\displaystyle \lim_{x 	o 3} f(x) = 2$$

Question 4

What is the value of $$f(4)$$ based on the graph?

Accepted Answer

$$2$$

Question 5

Evaluate $$\displaystyle \lim_{x 	o 4^-} f(x)$$ using the graph.

Accepted Answer

$$2$$

Question 6

Evaluate $$\displaystyle \lim_{x 	o 4^+} f(x)$$ using the graph.

Accepted Answer

$$2$$

Question 7

Does $$\displaystyle \lim_{x 	o 1} f(x)$$ exist? If so, what is its value?

Accepted Answer

Yes, the limit exists and is $$1$$

Question 8

Which of the following best describes the behavior of $$f(x) as$$ $$x$$ approaches $$2$$ from the left?

Accepted Answer

$$f(x)$$ approaches $$2$$

Question 9

If a two-sided limit exists at $$x = a$$, which of the following must be true?

Accepted Answer

$$\displaystyle \lim_{x 	o a^-} f(x) = \lim_{x 	o a^+} f(x)$$

Question 10

Which of the following is true about the value of $$f(1)$$?

Accepted Answer

$$f(1) = 2$$

Question 11

Suppose a business’s profit function is modeled by $$f(x) as $$shown in the graph. If $$x$$ represents the number of units sold, what does $$\displaystyle \lim_{x 	o 2} f(x)$$ represent in this context?

Accepted Answer

The expected profit as the number of units sold approaches $$2$$

Limits and One-Sided Limits in Calculus

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