Problem Set - Evaluating Limits when x goes to infinity

## Evaluating Limits when $x\to \infty$
 Evaluate $\underset{x\to \infty }{lim}\frac{x+2}{x-2}$. Evaluate $\underset{x\to \infty }{lim}\frac{3{x}^{2}+2x-5}{5{x}^{2}+3x+1}$. Evaluate $\underset{x\to \infty }{lim}\frac{{x}^{2}-7x+11}{3{x}^{2}+10}$. Evaluate $\underset{x\to \infty }{lim}\frac{2{x}^{3}-5x+7}{7{x}^{3}+{x}^{2}-6}$. Evaluate $\underset{x\to \infty }{lim}\frac{2{x}^{3}-5x+7}{7{x}^{3}+{x}^{2}-6}$. Evaluate $\underset{x\to \infty }{lim}\frac{\left(3x-1\right)\left(4x-5\right)}{\left(x-6\right)\left(x-3\right)}$. Evaluate $\underset{n\to \infty }{lim}\left(\frac{1}{3}+\frac{1}{{3}^{2}}+\frac{1}{{3}^{3}}+\dots +\frac{1}{{3}^{n}}\right)$. Evaluate $\underset{x\to \infty }{lim}\frac{x}{\sqrt{4{x}^{2}-1}-1}$. Evaluate $\underset{x\to -\infty }{lim}{2}^{x}$. Evaluate $\underset{n\to \infty }{lim}{\left(1+\frac{1}{n}\right)}^{n}$. Evaluate $\underset{t\to \infty }{lim}\frac{t+1}{{t}^{2}+1}$. Evaluate $\underset{n\to \infty }{lim}\sqrt{{n}^{2}+1}+n$. Evaluate $\underset{n\to \infty }{lim}\sqrt{{n}^{2}+n}+n$.