Question

Помогите, пожалуйста, решить пределы!

Answer 1

$displaystylelim_{x to 4} frac{2x^2-7x-4}{2x^2-13x+20}=frac{0}{0}=lim_{x to 4} frac{(x-4)(2x+1)}{(x-4)(2x-5)}=lim_{x to 4} frac{2x+1}{2x-5}=3$

$displaystylelim_{x to infty}(frac{x+1}{x-1})^{2x+1}=frac{infty}{infty}^infty=lim_{x to infty}(frac{x-1+2}{x-1})^{2x+1}=\=lim_{x to infty}(1+frac{2}{x-1})^{2x+1}=lim_{x to infty}[(1+frac{1}{frac{x-1}{2}})^frac{x-1}{2}}]^frac{4x+2}{x-1}}=e^{displaystylelim_{x to infty}frac{4x+2}{x-1}}=\=e^{displaystylelim_{x to infty}frac{x(4+frac{2}{x}^{to0})}{x(1-frac{1}{x}^{to0})}}=e^4$