1) 2
2) -2
3) 1
4) -1
5) 0
Solution: (2) -2
\(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow \infty} \frac{2 x-1}{\sqrt{x^{2}+2 x+1}}\\ \text { Replace } x \text { by }-t\\ \Rightarrow \lim _{t \rightarrow \infty} \frac{2(-t)-1}{\sqrt{(-t)^{2}+2(-t)+1}}\\ \Rightarrow \lim _{t \rightarrow \infty} \frac{-2 t-1}{\sqrt{t^{2}-2 t+1}}\\ \Rightarrow \lim _{t \rightarrow \infty} \frac{t\left(-2-\frac{1}{t}\right)}{t \sqrt{1-\frac{2}{t}+\frac{1}{t^{2}}}}\\ \Rightarrow \lim _{t \rightarrow \infty} \frac{-2-\frac{1}{t}}{\sqrt{1-\frac{2}{t}+\frac{1}{t^{2}}}}\\ \text { As } t \rightarrow \infty \frac{1}{t} \rightarrow 0\\ \Rightarrow \frac{-2-0}{\sqrt{1-0+0}}=-2 \end{array}\end{array} \)
