Question

D%7B%20%5Csqrt%7Bx%5E2%20-%204%7D%20%2B2%7D" id="TexFormula1" title=" \lim_{x \to \00} \frac{ \sqrt{ x^{2}+ 16 } -4}{ \sqrt{x^2 - 4} +2}" alt=" \lim_{x \to \00} \frac{ \sqrt{ x^{2}+ 16 } -4}{ \sqrt{x^2 - 4} +2}" align="absmiddle" class="latex-formula">
This is a 30 point offer. Please answer it fully and explain how you solved it.

Answer 1

$\lim_{x \to 0}\frac{-4 + \sqrt{x^{2} + 16}}{2 + \sqrt{x^{2} - 4}}$
$\lim_{x \to 0}\frac{4 + \sqrt{(0)^{2} + 16}}{2 + \sqrt{(0)^{2} - 4}}$
$\lim_{x \to 0}\frac{4 + \sqrt{0 + 16}}{2 + \sqrt{0 - 4}}$
$\lim_{x \to 0} = \frac{4 + \sqrt{16}}{2 + \sqrt{-4}}$
$\lim_{x \to 0} = \frac{4 + 4}{2 + 2i}$
$\lim_{x \to 0} = \frac{8}{2 + 2i}$
$\lim_{x \to 0} = \frac{2(4)}{2(1) + 2(i)}$
$\lim_{x \to 0} = \frac{2(4)}{2(1 + i)}$
$\lim_{x \to 0} = \frac{4}{1 + i}$