Question

Compute the following limits:
lim x->2
$(3 {x}^{2} + 3x - 18) \(x - 2)$
lim h->0
$\sqrt{h + 1} - 1 \div h$
​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr2} \frac{3 {x}^{2} + 3x - 18 }{x - 2}$

$= \lim_{x \rarr2} \frac{3 {x}^{2} + 9x - 6x - 18 }{x - 2}$

$= \lim_{x \rarr2} \frac{3x(x + 3) - 6(x +3) }{x - 2}$

$= \lim_{x \rarr2} \frac{(3x - 6)(x + 3) }{x - 2}$

$= \lim_{x \rarr2} \frac{3(x - 2)(x + 3) }{x - 2}$

$= \lim_{x \rarr2} 3(x + 3)$

$= 3(2 + 3)$

$= 15$