Question

resolva e explique
lim ([raiz] x+3) - ([raiz] 3) / x
x->0

Answer 1

Seria: $\lim_{x \to \ 0} \frac{ \sqrt{3+x} - \sqrt{3} }x}$ ?

$\lim_{x \to \ 0} \frac{ \sqrt{3+x} - \sqrt{3} }x} . \frac{(\sqrt{3+x} + \sqrt{3})}{(\sqrt{3+x} + \sqrt{3})}$

$\lim_{x \to \ 0} \frac{3+x-3}{x(( \sqrt{3+x}) + \sqrt{3} )}$

$\lim_{x \to \ 0} \frac{x}{x(( \sqrt{3+x}) + \sqrt{3} )}$ elimina o x do numerador e denominador

$\lim_{x \to \ 0} \frac{1}{(( \sqrt{3+x}) + \sqrt{3} )}$

substitui o valor de x

$\lim_{x \to \ 0} \frac{1}{(( \sqrt{3+0}) + \sqrt{3} )}$

$\lim_{x \to \ 0} \frac{1}{ \sqrt{3} + \sqrt{3} }$

$\lim_{x \to \ 0} \frac{1}{ 2\sqrt{3} }$

$\lim_{x \to \ 0} \frac{ \sqrt{3+x} - \sqrt{3} }x} = \frac{1}{ 2\sqrt{3} }$