Question

Cât este lim x-> infinit din radical de ordin x din x

Answer 1

Răspuns:

egal cu 1.............

Answer 2

$\lim_{x \to \infty} \sqrt[x]{x} \\a^b=e^{ln(a)^b}=e^{b*ln(a)}\\ \lim_{x \to \infty} \sqrt[x]{x}= \lim_{x \to \infty} x^{\frac{1}{x}} \\a=x\\b=\frac{1}{x}\\ \lim_{x \to \infty} x^{\frac{1}{x}} =\lim_{x \to \infty} e^{\frac{1}{x}lnx}}=e^{ \lim_{x \to \infty}\frac{1}{x}lnx}=L\\ \lim_{x \to \infty}\frac{lnx}{x}=\lim_{x \to \infty}\frac{(lnx)'}{x' }=\lim_{x \to \infty}\ \frac{1}{x}=\frac{1}{+\infty}=0\\ L=e^{ \lim_{x\to \infty} \frac{1}{x}lnx }=e^o=1\\ \lim_{x \to \infty} \sqrt[x]{x}=1$