Problem Set - Evaluating Limits when x goes to 0

## Problem Set - Evaluating Limits when $x\to 0$

Last updates: 7 December 2009

## Evaluating Limits when $x\to 0$

 Evaluate $\underset{x\to 0}{lim}{\left({x}^{2}-2\right)}^{2}+6$. Evaluate $\underset{x\to 0}{lim}\frac{5x}{x}$. Evaluate $\underset{x\to 0}{lim}\frac{17x}{2x}$. Evaluate $\underset{x\to 0}{lim}\frac{-317x}{422x}$. Evaluate $\underset{x\to 0}{lim}\frac{-317x-3}{422x+5}$. Evaluate $\underset{h\to 0}{lim}\frac{\sqrt{x+h}-\sqrt{x}}{h}$. Evaluate $\underset{x\to 0}{lim}\frac{\sqrt{1+x+{x}^{2}}-1}{x}$. Evaluate $\underset{x\to 0}{lim}\frac{\sqrt{2+x}-\sqrt{2}}{x}$. Evaluate $\underset{h\to 0}{lim}\frac{1}{h}\left(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}\right)$. Evaluate $\underset{x\to 0}{lim}\frac{2x}{\sqrt{a+x}-\sqrt{a-x}}$. Evaluate $\underset{x\to 0}{lim}\frac{\sqrt{1+x}-1}{x}$. Evaluate $\underset{x\to 0}{lim}\frac{x}{\sqrt{1+x}-1}$. Evaluate $\underset{x\to 0}{lim}\frac{{e}^{x}+{e}^{-x}-2}{{x}^{2}}$. Evaluate $\underset{\Delta x\to 0}{lim}\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\left(x+\Delta x\right)-x}$, when $f\left(x\right)=\sqrt{ax+b}$. Evaluate $\underset{\Delta x\to 0}{lim}\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\left(x+\Delta x\right)-x}$, when $f\left(x\right)={\left(mx+c\right)}^{n}$.