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Let $\lim_{x \to 1}(v(x))=$ . 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))=

. find

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

and

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

Consider Behavior: To find $\lim_{x \to 1^+}(v(x))$ , we need to consider the behavior of $v(x)$ as $x$ gets closer to $1$ from values greater than $1$ .
Limit Calculation: Since we're not given a specific function for $v(x)$ , we can't calculate the exact limit. However, we can say that if $\lim_{x \to 1}(v(x))$ exists and equals some value $L$ , then $\lim_{x \to 1+}(v(x))$ should also equal $L$ , unless there's a discontinuity.
Behavior Analysis: Similarly, to find $\lim_{x \to 1^-}v(x)$ , we need to consider the behavior of $v(x)$ as $x$ gets closer to $1$ from values less than $1$ .
Limit Existence: Again, without a specific function for $v(x)$ , we can't find the exact limit. But if $\lim_{x \to 1}(v(x))$ exists and equals $L$ , then $\lim_{x \to 1^-}(v(x))$ should also equal $L$ , unless there's a discontinuity.
Discontinuity Consideration: Since we know that $\lim_{x \to 1}(v(x)) = .$ , we can assume that both $\lim_{x \to 1^+}(v(x))$ and $\lim_{x \to 1^-}(v(x))$ are also $.$ , unless we're told otherwise about a discontinuity.

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