Question

$\huge\underline\mathrm\red{Question:-}$
$\displaystyle \lim_{x \to 2} \frac{x^2-4}{x-2}$ . find the value of x ​

Answer 1

Question :-

$\sf \: = \: \displaystyle \lim_{x \to 2} \frac{ {x}^{2} - 4}{x - 2}$ find the value of x

Solution :-

$\sf \: applying \: the \: formula \: = {x}^{2} - {a}^{2} = (x - a)(x + a )$

$\sf \: = \: \displaystyle \lim_{x \to 2} \frac{ {x}^{2} - 4}{x - 2}$

$\sf \: = \: \: \displaystyle \lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}$

$\sf \: cancel \: out \: the \: common \: term \:$

$\sf \: = \: \: \displaystyle \lim_{x \to 2} \frac{{ (\cancel{x-2}})(x + 2)}{ \: (\cancel{x - 2})}$

$\sf \: = \displaystyle \lim_{x \to 2} \: (x + 2) = 2$

therefore the value of x = 2

_____________________________________

$\sf \: substituting \: x = 2 \: into \: the \: (1) \: expression \:$

$\sf \: = \displaystyle \lim_{x \to 2} \: (x + 2) = 4$

value of expression = 4