Question

the limit as x approaches negative infinity the equation is (x-2)/((((x^2)+1))^.5)) i have no idea how to get the limit on this equation.

Answer 1

\[\lim_{x \rightarrow - \infty}\frac{x-2}{\sqrt{x^2+1}}*\frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\]
since x<0, then sqrt{x^2}=|x|=-x.
\[\lim_{x \rightarrow - \infty} \frac{-1-\frac{2}{\sqrt{x^2}}}{1+\sqrt{\frac{1}{x^2}}}\]
\[\lim_{x \rightarrow -\infty}\frac{-1+\frac{2}{x}}{1+\frac{1}{-x}}\]

Answer 2

=-1