Question

Does the limit exist? If the limit does exists what is the value?Calculus early transcendental functions

Answer 1

given

$\lim _{x\to\infty}\frac{x^2+2}{1-x-3x^2}$$\begin{gathered} \lim _{x\to\infty}\frac{x^2+2}{1-x-3x^2} \\ \lim _{x\to\infty}\frac{1+\frac{2}{x^2}}{\frac{1}{x^2}-\frac{x}{x^2}-3} \\ \lim _{x\to\infty}\frac{1+\frac{2}{x^2}}{\frac{1}{x^2}-\frac{1}{x}-3} \end{gathered}$

let x tends to infinty

$\begin{gathered} \lim _{x\to\infty}\frac{1+\frac{2}{x^2}}{\frac{1}{x^2}-\frac{1}{x}-3} \\ \frac{1+\frac{2}{\infty^2}}{\frac{1}{\infty^2}-\frac{1}{\infty}-3} \end{gathered}$

since ,1 divided by infinty is underfined.

limit does not exist.