Respuesta :

given

[tex]\lim _{x\to\infty}\frac{x^2+2}{1-x-3x^2}[/tex][tex]\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}[/tex]

let x tends to infinty

[tex]\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}[/tex]

since ,1 divided by infinty is underfined.

limit does not exist.

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