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  • Evaluate each of the following limits Let f(x)=x+2 & x \leq-1 c x^{2} if x>-1 find ‘c’ if \lim _{x \rightarrow-1} f(x) exists.

Evaluate each of the following limits

Let f(x)=\begin{array}{ll} x+2 & x \leq-1 \\ c x^{2} & x>-1 \end{array}

find ‘c’ if  \lim _{x \rightarrow-1} f(x) exists.

Answers (1)

\\ LHL=\mathop{\lim }_{x \rightarrow \mathop{-1}^{-}} \left( x+2 \right) =-1+2=1 \\ \\ RHL=\mathop{\lim }_{x \rightarrow \mathop{-1}^{+}}cx^{2}=c \\ \\ LHL=RHL \\ \\ c=1 \\ \\

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