Question

Determine the limit by factoring:
((2+x)^3-8)/x

Answer 1

\[(a^3-b^3)=(a-b)(a^2+ab+b^2)\]so\[\frac{(x+2)^3-2^3}{x}=\frac{((x+2)-2)((x+2)^2+2(x+2)+4)}{x}=(x+2)^2+2(x+2)+4=\\x^2+4x+4+2x+4+4 =\\ x^2+6x+12\]
so
\[\lim_{x\rightarrow a}\frac{(x+2)^3-8}{x}=\lim_{x\rightarrow a}(x^2+6x+12)=a^2+6a+12\]

Answer 2

@lamp12345 understand?