If the function $ f(x) $ satisfies $ \lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\Pi $ then $ \lim _{x \rightarrow 1} f(x)= $

Question

If the function $ f(x) $ satisfies $ \lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\Pi $ then $ \lim _{x \rightarrow 1} f(x)= $, $ 02 $, $ 03 $, $ 11 $, $ 00 $

MARKS App · Accepted Answer

Given that, $ \lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\Pi \rightarrow(1) $ Clearly, if $ \lim _{x \rightarrow 1} f(x)=1 $ or $ 0 $ or $ 3 $. Then $ \lim _{x \rightarrow 1} \frac{f(x-2)}{x^{2}-1} $ doesn't exist, that is, contradicting Eq. (1). Hence, option (1) is the correct answer.

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