# Get help with limits and continuity

Recent questions in Limits and continuity
cristinamahumas 2022-01-14

2022-01-10

### Calculate the sum of the series $$\displaystyle\sum\infty{n}={1}$$ a n whose partial sums are given. $$\displaystyle{s}{n}={2}-{3}{\left({0.8}\right)}^{{n}}$$

Braxton Pugh 2021-10-22 Answered

### a) Using limit rules each of the following limits $$\displaystyle\lim_{{{x}\rightarrow{0}}}{\frac{{{x}+{1}}}{{{x}}}}$$ $$\displaystyle\lim_{{{x}\rightarrow{0}}}{\frac{{{x}+{1}}}{{{x}^{{{2}}}}}}$$ $$\displaystyle\lim_{{{x}\rightarrow{0}}}{\frac{{{x}}}{{{x}+{1}}}}$$ $$\displaystyle\lim_{{{x}\rightarrow{0}}}{\frac{{{x}+{1}}}{{{x}+{2}}}}$$ b) Using limit rules evaluate $$\displaystyle\lim_{{{x}\rightarrow{2}}}{\frac{{\sqrt{{{x}+{7}}}-{3}}}{{{x}-{2}}}}$$

Tammy Todd 2021-10-13 Answered

### Use the limit definition of the derivative to calculate the derivatives of the following function: (a) $$\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}+{3}{x}+{1}$$ (b) $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{2}}}{{{x}^{{2}}}}}$$

Efan Halliday 2021-09-07 Answered

### Find the following limits 1) $$\displaystyle\lim_{{{x}\to{0}}}\frac{{\tan{{\left({4}{x}\right)}}}}{{{x}+{\sin{{\left({2}{x}\right)}}}}}$$ 2) $$\displaystyle\lim_{{{x}\to\infty}}{\left({e}^{{{2}{x}}}+{x}\right)}^{{\frac{{1}}{{x}}}}$$

Nannie Mack 2021-08-12 Answered