Question

Să se calculeze:
a) $\lim_{x \to 0} \frac{ln(1+ x^{2} )}{5 x^{2} }$;
b) $\lim_{x \to 0} \frac{ln(1+ \sqrt[3]{x}) }{ \sqrt[3]{5x} }$.

Answer 1

Avem limita remarcabila $\lim_{u(x) \to \ 0} \frac{ln(1+u(x))}{u(x)}=1$
a) $\lim_{x \to \ 0} \frac{ln(1+ x^{2} )}{ x^{2} } \frac{1}{5}= \frac{1}{5}$
b)$\lim_{x \to \ 0} \frac{ln(1+ \sqrt[3]{x}) }{ \sqrt[3]{x} } \frac{1}{ \sqrt[3]{5} }= \frac{1}{ \sqrt[3]{5} }$