31.   If the function f(x) satisfies  \lim_{x \rightarrow 1} \frac{f (x)-2}{x^2-1} = \pi  , evaluate \lim_{x \rightarrow 1} f (x)

Answers (1)

Given

\lim_{x \rightarrow 1} \frac{f (x)-2}{x^2-1} = \pi

Now,

\lim_{x \rightarrow 1} \frac{f (x)-2}{x^2-1} = \frac{\lim_{x \rightarrow 1}(f (x)-2)}{\lim_{x \rightarrow 1}(x^2-1)}=\pi

{\lim_{x \rightarrow 1}(f (x)-2)}=\pi{\lim_{x \rightarrow 1}(x^2-1)}

{\lim_{x \rightarrow 1}(f (x)-2)}=\pi{(1-1)}

{\lim_{x \rightarrow 1}(f (x)-2)}=0

{\lim_{x \rightarrow 1}f (x)}=2

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