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Provide an Appropriate Response limxθf(x)=L,limxθ+f(x)=Lr\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = L , \lim _ { x - \theta ^ { + } } f ( x ) = L _ { r }

question 57

Multiple Choice

Provide an appropriate response.
-Given limxθf(x) =L,limxθ+f(x) =Lr\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = L , \lim _ { x - \theta ^ { + } } f ( x ) = L _ { r } , and L1=LrL _ { 1 } = L _ { r } , which of the following statements is false?
I. limx9f(x) =Ll\lim _ { x \rightarrow 9 } f ( x ) = L _ { l }
II. limxθf(x) =Lr\lim _ { x \rightarrow \theta } f ( x ) = L _ { r }
III. limxθf(x) \lim _ { x \rightarrow \theta } f ( x ) does not exist.

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