Question

Find the value of $\underset{x\to 3}{lim}\frac{\sqrt{16x^2+112}-16}{3x^2-15x+18}$

Answer 1

$li{m}_{x\to 3}\frac{\sqrt{16x^2+112}-16}{3x^2-15x+18}$
$=li{m}_{x\to 3}\frac{\sqrt{16x^2+112}-16}{3(x^2-5x+6)}\frac{\sqrt{16x^2+112}+16}{\sqrt{16x^2+112}+16}$
$=li{m}_{x\to 3}\frac{16(x^2-9)}{3(x-2)(x-3)}\frac{1}{\sqrt{16x^2+112}+16}$
$=li{m}_{x\to 3}\frac{16(x+3)}{3(x-2)}\frac{1}{\sqrt{16x^2+112}+16}$
$=\frac{16\left(6\right)}{3\left(1\right)}\frac{1}{32}=1$