Provide an appropriate response.
-Given $\lim _ { x \rightarrow 0 ^ { - } } \mathrm { f } ( \mathrm { x } ) = \mathrm { L } _ { \mathrm { l } } , \lim _ { \mathrm { x } - 0 ^ { + } } \mathrm { f } ( \mathrm { x } ) = \mathrm { L } _ { \mathrm { r } }$, and $\mathrm { L } \mathrm { l } \neq \mathrm { L } _ { \mathrm { r } }$, which of the following statements is true?
I. $\lim _ { x \rightarrow 0 } f ( x ) = L _ { l }$
II. $\lim _ { x \rightarrow 0 } f ( x ) = L _ { r }$
III. $\lim _ { x \rightarrow 0 } f ( x )$ does not exist.
A) I
B) none
C) II
D) III

Question

Quizplus · Accepted Answer

Since the left and right limits are not equal, the limit at x=0 does not exist. Therefore, statement III is true while statements I and II are false.

Provide an Appropriate Response , And Ll≠Lr\mathrm { L } \mathrm { l } \neq \mathrm { L } _ { \mathrm { r } }Ll=Lr​

Provide an Appropriate Response , And $\mathrm { L } \mathrm { l } \neq \mathrm { L } _ { \mathrm { r } }$