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

Provide an appropriate response.
-Given $\lim _ { x \rightarrow 0^ { - } } \mathrm { f } ( \mathrm { x } ) = \mathrm { L } _ { \mathrm { l } } , \lim _ { \mathrm { x } \rightarrow 0 ^ { + } } \mathrm { f } ( \mathrm { x } ) = \mathrm { L } _ { \mathrm { r } }$ , and $\mathrm { L } _ { \mathrm { l } } = \mathrm { L } _ { \mathrm { r } }$ , which of the following statements is false?
I. $\lim _ { x \rightarrow 0 } f ( x ) = L _ { 1 }$
II. $\lim _ { x \rightarrow0 } f ( x ) = L _ { r }$
III. $\lim _ { x \rightarrow 0} f ( x )$ does not exist.

A) II
B) none
C) III
D) I