Question

помогите решить два предела (фото внутри)

Answer 1

$lim_{x to infty} (1+frac{1}{3x})^x={3x=a, x=frac{1}{3}a, x to infty, a to infty } = \ lim_{x to infty} (1+frac{1}{a})^{frac{1}{3}a}=lim_{x to infty} ((1+frac{1}{a})^a)^{frac{1}{3}}= \ (lim_{x to infty} (1+frac{1}{a})^a)^{frac{1}{3}}=e^{frac{1}{3}=sqrt[3]{e}$

 

$lim_{x to infty} (1-frac{1}{4x})^{2x}={-4x=a, x=-frac{1}{4}a, x to infty, a to infty } = \ lim_{x to infty} (1+frac{1}{a})^{2cdot(-frac{1}{4}a)}=lim_{x to infty} ((1+frac{1}{a})^a)^{-frac{1}{2}}= e^{-frac{1}{2}}=frac{1}{sqrt{e}}$