No, because $$\displaystyle \lim_{x \to 1^-} f(x) \neq \lim_{x \to 1^+} f(x)$$

$$\displaystyle \lim_{x \to 0^-} f(x) = 0$$

$$\displaystyle \lim_{x \to 0^+} f(x) = 1$$

Question 1

Given the graph above for $$y = f(x)$$, what is the value of $$\displaystyle \lim_{x 	o 1^-} f(x)$$?

Accepted Answer

$$2$$

Question 2

Given the graph above for $$y = f(x)$$, what is the value of $$\displaystyle \lim_{x 	o 1^+} f(x)$$?

Accepted Answer

$$0$$

Question 3

Given the graph above for $$y = f(x)$$, what is the value of $$f(1)$$?

Accepted Answer

$$3$$

Question 4

Given the graph above for $$y = f(x)$$, which of the following best describes the type of discontinuity at $$x = 1$$?

Accepted Answer

Removable discontinuity

Question 5

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

Accepted Answer

$$1.5$$

Question 6

Given the graph above for $$y = f(x)$$, is $$f(x)$$ continuous at $$x = 1$$?

Accepted Answer

No, because $$\displaystyle \lim_{x 	o 1^-} f(x) 
eq \lim_{x 	o 1^+} f(x)$$

Question 7

Given the graph above for $$y = f(x)$$, which of the following statements is true?

Accepted Answer

$$f(x)$$ has a removable discontinuity at $$x = 1$$

Question 8

Given the graph above for $$y = f(x)$$, which of the following best describes the left-hand limit at $$x = 0$$?

Accepted Answer

$$\displaystyle \lim_{x 	o 0^-} f(x) = 0$$

Question 9

Given the graph above for $$y = f(x)$$, which of the following best describes the right-hand limit at $$x = 0$$?

Accepted Answer

$$\displaystyle \lim_{x 	o 0^+} f(x) = 1$$

Question 10

Given the graph above for $$y = f(x)$$, does $$\displaystyle \lim_{x 	o 0} f(x)$$ exist?

Accepted Answer

No, because the left and right limits are not equal

Calculus I Test 1 Review: Limits, Continuity, Asymptotes, Derivatives

Study Guide - Practice Questions