Question

lim(x=>3-) (x^2 - 9) / |x-3| = y ; find y .plz show step by step

Answer 1

Step-by-step explanation:

We have,

$= \lim_{x \rarr3 - } \frac{ {x}^{2} - 9}{ |x - 3| }$

$= \lim_{h\rarr0} \frac{((3 - h) ^{2} - 9) }{ |3 -h - 3| }$

$= \lim_{h\rarr0} \frac{9 + {h}^{2} - 6h - 9}{ | - h| }$

$= \lim_{h\rarr0} \frac{h(h - 6)}{h}$

$= \lim_{h\rarr0}(h - 6)$

$= - 6$