Question

lim
x -> -∞ x-2/x^2 + 2x + 1

Answer 1

zero since the degree of denominator is larger

Answer 2

\[\lim_{x \rightarrow -\infty}\frac{x-2}{x^{2}+2x+1} = \lim_{x \rightarrow -\infty}\frac{\frac{1}{x^{2}}(x-2)}{\frac{1}{x^{2}}(x^{2}+2x+1)} \]
\[=\lim_{x \rightarrow -\infty}\frac{\frac{1}{x}-\frac{2}{x^{2}}}{1+\frac{2}{x}+\frac{1}{x^{2}}} = \frac{0}{1} =0\]

Answer 3

i agree, its gonna limit towards the horizontal asymptote