Question

предел функции как решить?

Answer 1

$large \ lim_{xrightarrow {-1}}{x^3+1 over x^2-1}=lim_{xrightarrow -1}{x^3+1 over (x-1)(x+1)}=lim_{xrightarrow -1}{(x+1)(x^2-x+1) over (x-1)(x+1)}=lim_{xrightarrow -1}{x^2-x+1 over x-1}=-{3over2}\\ lim_{xrightarrow 3}{x^2-2x-3over x^2-9}=lim_{xrightarrow 3}{(x^2-6x+9)+(-12+4x)over (x-3)(x+3)}=lim_{xrightarrow 3}{(x-3)+(4x-12)over (x-3)(x+3)}=lim_{xrightarrow 3}{(x-3)^2+4(x-3)over (x-3)(x+3)}=lim_{xrightarrow 3}{x-3over x+3}+4lim_{xrightarrow 3}{1over x+3}=0+{4over6}={2over3}\\ lim_{xrightarrow infty}{4x^2over x^2-1}=begin{pmatrix} {inftyover infty}Rightarrow div x^2 end{pmatrix}=4lim_{xrightarrow infty}{1over 1-{1over x^2}}=4$