Question

EVALUATE USING ALGEBRA LIM X^2 +2 / X -1 AS X GOES TO NEGATIVE INFINITY

Answer 1

The strategy for solving this is the same as the one I solved before, except the square root is gone and the limit boundary is negative infinity which will change the answer.
\[\lim_{x \rightarrow -\infty}(x^{2}+2)/(x-1)\] (factor out x^2 in the numerator and x in denominator)
\[\lim_{x \rightarrow -\infty}x^{2}(1+2/x^{2})/x(1-1/x) \]
\[\lim_{x \rightarrow -\infty}x(1+2/x^{2})/(1-1/x)\]
\[\lim_{x \rightarrow -\infty}x(1+0)/(1+0) \]
\[\lim_{x \rightarrow -\infty}x=-\infty\]
So the limit is \[-\infty\]