Question

помогите решить пределы

Answer 1

$lim_{x to 0} frac{Cos3x-(Cos3x)^3}{3x^2} = lim_{x to 0} frac{Cos3x(1-(Cos3x)^2)}{3x^2} =$$lim_{x to 0} frac{3Cos3x(Sin3x)^2}{(3x)^2}= [tex]|y=3x y to 0 x to 0|=3lim_{x to 0}Cos3x * (lim_{y to 0} frac{Siny}{y})^2$=[/tex]$=3*Cos(3*0)*1^2=3*Cos0*1=3*1*1=3$

$lim_{x to -5} frac{2x^2-50}{x+5} =2lim_{x to -5} frac{x^2-25}{x+5}=2lim_{x to -5} frac{(x+5)(x-5)}{x+5}$$=2lim_{x to -5}(x-5)=2(-5-5)=2*(-10)=-20$