Question

Calcule, se existirem, os seguintes limites:

Answer 1

Resposta:

$\sf \lim _{x\to 2}\left(\sqrt{\dfrac{x^3+2x+3}{x^2+5}}\right) = \sqrt{\dfrac{5}{3}}$

Explicação passo-a-passo:

$\sf \lim _{x\to 2}\left(\sqrt{\dfrac{x^3+2x+3}{x^2+5}}\right)$

$\sf \lim _{x\to 2}\left(\sqrt{\dfrac{2^3+2 \cdot 2+3}{2^2+5}}\right)$

$\sf \lim _{x\to 2}\left(\sqrt{\dfrac{8 +4+3}{4 + 5}}\right)$

$\sf \lim _{x\to 2} \sqrt{\dfrac{15}{9}}$

$\sf \lim _{x\to 2} \sqrt{\dfrac{5}{3}}$

Explicação passo-a-passo:

Answer 2

Limites

• Cálculo:

$\boxed{\large \sf \lim_{x \to 2} \sqrt{\dfrac{x^{3}+2x+3}{x^{2}+5} }}$

• Substitua x por 2:

$\boxed{\begin{array}{lr}\\\large \sf \lim_{x \to 2} \sqrt{\dfrac{2^{3}+2\cdot2+3}{2^{2}+5} }\\\\\\\large \sf \lim_{x \to 2} \sqrt{\dfrac{8+4+3}{4+5}}\\\\\\\large \sf \lim_{x \to 2} \sqrt{\dfrac{15}{9} } \\ \: \end{array}}$

• Simplifique a Fração:

$\boxed{\large \sf \lim_{x \to 2} \sqrt{\dfrac{15^{\div3}}{9^{\div3} }}=\dfrac{5}{3} }$

Resposta:

$\boxed{\boxed{\huge \sf \lim_{x \to 2} \sqrt{\dfrac{5}{3} }}}$