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Let $\lim_{x \to 1}(v(x))=2$ . find $\lim_{x \to 1+}(v(x))$ and $\lim_{x \to 1-}(v(x))$

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Determine end behavior of polynomial and rational functions

Full solution

Q. Let

\lim_{x \to 1}(v(x))=2

. find

\lim_{x \to 1+}(v(x))

and

\lim_{x \to 1-}(v(x))

Given Limit Information: To find $\lim_{x \to 1^+}(v(x))$ , we consider the given information that $\lim_{x \to 1}(v(x)) = 2$ . This implies that as $x$ approaches $1$ from the right, the limit of $v(x)$ should also be $2$ .
Limit as $x$ approaches $1+$ : So, $\lim_{x \to 1+}(v(x)) = 2$ .
Limit as $x$ approaches $1-$ : Similarly, to find $\lim_{x \to 1-}v(x)$ , we use the given information that $\lim_{x \to 1}v(x)=2$ . This implies that as $x$ approaches $1$ from the left, the limit of $v(x)$ should also be $2$ .
Conclusion: Therefore, $\lim_{x \to 1^-}(v(x)) = 2$ .

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