Provide an appropriate response.
-If $\lim _ { x \rightarrow 0 } f ( x ) = L$, which of the following expressions are true?
I. $\lim _ { x \rightarrow 0 ^ { - } } f ( x )$ does not exist.
II. $\lim _ { x \rightarrow0 ^ { + } } f ( x )$ does not exist.
III. $\lim _ { x \rightarrow0 ^ { - } } f ( x ) = L$
IV. $\lim _ { x \rightarrow0 ^ { + } } f ( x ) = L$
A) I and II only
B) II and III only
C) III and IV only
D) I and IV only

Question

Quizplus · Accepted Answer

Since we are given that the limit of f(x) as x approaches 0 exists and equals L, both the left and right limit must exist and be equal to L. Therefore, III and IV are true. However, there is no information given about the left and right limits approaching from the negative or positive side, so we cannot determine if either I or II are true. Therefore, the correct answer is C, which includes only III and IV.

Provide an Appropriate Response lim⁡x→0f(x)=L\lim _ { x \rightarrow 0 } f ( x ) = Llimx→0​f(x)=L

Provide an Appropriate Response $\lim _ { x \rightarrow 0 } f ( x ) = L$