Question

limit x to 1 x-1/×^2-1​

Answer 1

$\bf \LARGE \color{pink}Hola!$

To FinD :

$\rightsquigarrow \sf \: \: \: \lim_{x\to1} \frac{x - 1}{ {x}^{2} - 1 } = {?}$

SolutioN :

$\circ \: \: \sf \: If \: \: we \: \: substitute \: \: the \: \: limiting \: \: value \: \: the \: \: function \: \: will \: \: be \: \: a \: \: undefined \: \: form \: \frac{0}{0}$

$\: \: \: \: \: \circ \sf \: \: \: \: \: \lim_{x\to1}f(x) = \: \lim_{x\to1} \frac{x - 1}{ {x}^{2} - 1 }$

$\ \implies \sf \lim_{x\to1}f(x) = \: \lim_{x\to1} \frac{x - 1}{ ({x}^{} - 1 )(x + 1)}$

$\ \implies \sf \lim_{x\to1} \: f(x) = \: \lim_{x\to1} \frac {\cancel{{(x - 1)}}}{ \cancel{ ({x}^{} - 1 )}(x + 1)}$

$\ \implies \sf \lim_{x\to1} \: f(x) = \: \lim_{x\to1} \frac {1}{(x + 1)}$

Putting limiting value,

$\ \implies \sf \lim_{x\to1} \: f(x) = \: \frac {1}{(1+ 1)}$

$\ \implies \underline{ \boxed{\sf \lim_{x\to1} \: f(x) = \: \frac {1}{2} }}$

____________________

HOPE THIS IS HELPFUL...

$\tt \fcolorbox{skyblue}{skyblue}{@StayHigh}$