Question

Limites indeterminados, me ajudem

Answer 1

Oi, Branca :)  . Aí está: 
$\lim_{x \to -3} \sqrt[3]{ \frac{x-4}{6x^2+2} } \\ \\ \lim_{x \to -3} \sqrt[3]{ \frac{-3-4}{6(-3)^2+2} } \\ \\ \lim_{x \to -3} \sqrt[3]{ \frac{-7}{56} } \\ \\ \lim_{x \to -3} \sqrt[3]{ \frac{-1}{8} } \\ \\ \lim_{x \to -3} { \frac{ \sqrt[3]{-1} }{ \sqrt[3]{8} } \\ \\ \lim_{x \to -3} { \frac{ \sqrt[3]{-1} }{ 2 } \\ \\ \lim_{x \to -3} { \frac{ 1 }{ 2 }$
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$\lim_{h \to 0} \frac{(3+h)^2+9}{h} \\ \\ \lim_{h \to 0} \frac{9+6h+h^2+9}{h} \\ \\ \lim_{h \to 0} \frac{6h+h^2}{h} \\ \\ \lim_{h \to 0} 6+h \\ \\ \lim_{h \to 0} 6+0 \\ \\ \lim_{h \to 0} 6$
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$\lim_{x \to 0} \frac{ \sqrt{x+2}- \sqrt{2} }{x} \\ (racionalizando) \\ \lim_{x \to 0} \frac{ - \sqrt{2} +\sqrt{x+2} }{x}\frac{ \sqrt{2}+\sqrt{x+2} }{\sqrt{2}+\sqrt{x+2} } \\ \\ \lim_{x \to 0} \frac{ x+2-2 }{x(\sqrt{2}+\sqrt{x+2} )} \\ \\ \lim_{x \to 0} \frac{1 }{\sqrt{2}+\sqrt{x+2}} \\ \\ \lim_{x \to 0} \frac{1 }{\sqrt{2}+\sqrt{0+2}} \\ \\ \lim_{x \to 0} \frac{1 }{\sqrt{2}+\sqrt{2}}} \\ \\ \lim_{x \to 0} \frac{1 }{2\sqrt{2}}} \\ (racionalizando)$
$\lim_{x \to 0} \frac{1 }{2\sqrt{2}}}.\frac{ \sqrt{2} }{\sqrt{2}}} \\ \\ \lim_{x \to 0} \frac{ \sqrt{2} }{2*2}} \\ \\ \lim_{x \to 0} \frac{ \sqrt{2} }{4}}$