Question

Помогите решить пожалуйста

Answer 1

1)
$lim_{xto3}(frac{x^2-6x+9}{x^2-3x})=lim_{xto3}(frac{(x-3)^2}{x(x-3)})=lim_{xto3}(frac{x-3}{x})=frac{3-3}{3}=0$


2)
$lim_{xto2}(5x^3+4x^2-5x+2)=5*2^3+4*2^2-5*2+2=48$


3)
$lim_{xtoinfty}(frac{5x^3+x-1}{2x^3+5x^2})=lim_{xtoinfty}(frac{x(5x^2+1)}{x^2(2x+5)})=lim_{xtoinfty}(frac{5x^2+1}{x(2x+5)})=\=lim_{xtoinfty}(frac{5x^2}{x(2x+5)})=lim_{xtoinfty}(frac{5x}{2x+5})=lim_{xtoinfty}(frac{5x}{2x})=frac{5}{2}$


4)
$lim_{xtoinfty}(1+frac{2}{x})^{2x}=e^{lim_{xtoinfty}((1+frac{2}{x})-1)*2x)}=e^{lim_{xtoinfty}(frac{2}{x}*2x})=e^4$


5)
$lim_{hto0}frac{(x+h)^3-x^3}{h}=[frac{0}{0}]=lim_{hto0}frac{((x+h)^3-x^3)'}{(h)'}=lim_{hto0}frac{3(x+h)^2}{1}=3x^2$