求极限 $$ex lim_{x o +infty} sex{sqrt[6]{x^6+x^5}-sqrt[6]{x^6-x^5}}. eex$$
解答: $$eex ea mbox{原极限}&=lim_{x o+infty}xsex{sqrt[6]{1+frac{1}{x}}-sqrt[6]{1-frac{1}{x}}}\ &=lim_{t o 0}frac{sqrt[6]{1+t}-sqrt[6]{1-t}}{t}quadsex{frac{1}{x}lra t}\ &=lim_{t o 0}frac{frac{1}{6}(1+xi_t)^{-frac{5}{6}}cdot 2t}{t} quadsex{f(t)=sqrt[6]{1+t} a f(t)-f(-t)=f'(xi_t)cdot 2t}\ &=frac{1}{3}. eea eeex$$