Question
If $\lim _{x \rightarrow 1^{-}} f(x)=5$ and $\lim _{x \rightarrow 1^{+}} f(x)=5,$ what can you say about $\lim _{x \rightarrow 1} f(x) ?$ What can you say about $f(1) ?$
Step 1
Step 1: We are given that the left hand limit of the function as x approaches 1 is 5, which is mathematically represented as $\lim _{x \rightarrow 1^{-}} f(x)=5$. Show more…
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$$ \begin{array}{l} \text { If } \lim _{x \rightarrow 1^{-}} f(x)=5 \text { and } \lim _{x \rightarrow 1^{+}} f(x)=5, \text { what can you say about }\\ \lim _{x \rightarrow 1} f(x) ? \text { What can you say about } f(1) \text { ? } \end{array} $$
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$$ \begin{array}{l} \text { If } \lim _{x \rightarrow-1+} f(x)=-\infty \text { and } \lim _{x \rightarrow-1^{-}} f(x)=-\infty, \text { what can you }\\ \text { say about } \lim _{x \rightarrow-1} f(x) \text { ? } \end{array} $$
If $\lim _{x \rightarrow-1^{+}} f(x)=-\infty$ and $\lim _{x \rightarrow-1^{-}} f(x)=-\infty,$ what can you say about $\lim _{x \rightarrow-1} f(x) ?$
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