Question

Помогите решить данные примеры

Answer 1

$1); limlimits _{x to 2,5}frac{42}{2x-5}=Big [frac{42}{0}Big]=infty \\\2); limlimits _{x to 0}frac{4x^3-3x^2}{2x^2+5x}=limlimits _{x to 0}frac{x^2, (4x-3)}{x, (2x+5)}=limlimits _{x to 0}frac{x(4x-3)}{2x+5}=0$

$3); limlimits _{x to infty}frac{x^4+x^5}{x^2+x^3}=limlimits _{x to infty}frac{x^5}{x^3}=limlimits _{x to infty}x^2=infty \\\4); limlimits _{x to 0}frac{sin3x}{sin5x}=limlimits _{x to 0}frac{3x}{5x}=frac{3}{5}$

$5); limlimits _{x to 0}(1-x)^{1/x}=Big [1^{infty }Big]=limlimits _{x to 0}Big (Big (underbrace {1+(-x)Big)^{frac{1}{-x}}}_{to ; e}Big )^{-1}=e^{-1}$