Question

Sabendo que $\lim_{x \to \ 1} f(x) = \lim_{x \to \ 1} g(x) = 2$
Determine:
$L= \frac{ \lim_{x \to \ 1} f(x)^{2} - \lim_{x \to \ 1} g(x)^{2}}{lim_{x \to \ 1} f(x)^{4} - lim_{x \to \ 1} g(x)^{4}}$

Answer 1

Resposta:

L = 1/8

ou

L = 0,125

Explicação passo a passo:

$\lim_{x \to 1} f(x)=2\\\\ \lim_{x \to 1} g(x)=2\\\\\\\\L=\frac{ \lim_{x \to 1} f(x)^{2} - \lim_{x \to 1} g(x)^{2}}{ \lim_{x \to 1} f(x)^{4} - \lim_{x \to 1} g(x)^{4} } \\\\\\\\Substituir\ \bold{\lim_{x \to 1} f(x)} \ por\ \bold{2}\ e\ \bold{\lim_{x \to 1} g(x)}\ por\ \bold{2}\\\\\\\\L=\frac{ 2^{2} - 2^{2}}{ 2^{4} - 2^{4} }\\\\L=\frac{2^{2} - 2^{2}}{(2^{2}-2^{2})(2^{2}+2^{2})}\\\\L=\frac{1}{2^{2}+2^{2} }\\\\L=\frac{1}{4+4} \\\\\bold{L=\frac{1}{8} }$