Find the limit of (x^3)/(x^2+2)-x as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(\frac{x^3}{x^2+2}-x\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(\frac{x^3}{x^2+2}-x\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{\infty ^3}{\infty ^2+2}- \infty $

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^3=\infty$

$\frac{\infty }{\infty +2}- \infty $

 

Infinity plus any algebraic expression is equal to infinity

$\frac{\infty }{\infty }- \infty $

 

Infinity divided by infinity ($\frac{\infty}{\infty}$) is an indeterminate form

indeterminate

indeterminate

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