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

question 104

Multiple Choice

Provide an appropriate response.
-Given limx0f(x) =Ll,limx0+f(x) =Lr\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 LlLr\mathrm { L } \mathrm { l } \neq \mathrm { L } _ { \mathrm { r } } , which of the following statements is true?
I. limx0f(x) =Ll\lim _ { x \rightarrow 0 } f ( x ) = L _ { l }
II. limx0f(x) =Lr\lim _ { x \rightarrow 0 } f ( x ) = L _ { r }
III. limx0f(x) \lim _ { x \rightarrow 0 } f ( x ) does not exist.

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