Question

Solve:

${lim}_{x\to \infty }\frac{x^3}{(x^2+1)(x+1)}$

Answer 1

We have,

${lim}_{x\to \infty }\frac{x^3}{(x^2+1)(x+1)}$

${lim}_{x\to \infty }\frac{x^3}{x^3+x^2+x+1}$

${lim}_{x\to \infty }\frac{x^3}{x^3(1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3})}$

${lim}_{x\to \infty }\frac{1}{(1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3})}$

$=\frac{1}{(1+0+0+0)}$

$=1$

Hence, this is the answer.