Limits and continuity questions and answers

Recent questions in Limits and continuity
Limits and continuity

Evaluate $$\displaystyle\lim_{{{x}\rightarrow\infty}}{\frac{{{\sin{{h}}}{x}}}{{{e}^{{x}}}}}$$

Limits and continuity

Please, find the $$\displaystyle\lim{i}{t}\lim_{{{x}\to-{1}}}{\left({\frac{{{\left({x}+{1}\right)}^{{2}}{\left({x}-{1}\right)}}}{{{x}^{{3}}+{1}}}}\right)}$$

Limits and continuity

Prove using the definition on the limit that $$\displaystyle\lim_{{{n}\to\infty}}{\frac{{{1}+{n}}}{{{1}-{2}{n}}}}={\frac{{-{1}}}{{{2}}}}$$

Limits and continuity

Which of the following is NOT a conclusion of the Central Limit​ Theorem? Choose the correct answer below. a) The distribution of the sample means x over bar x ​will, as the sample size​ increases, approach a normal distribution. b) The distribution of the sample data will approach a normal distribution as the sample size increases. c) The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size. d) The mean of all sample means is the population mean $$\mu$$

Limits and continuity

Evaluate $$\lim_{x \rightarrow \infty} \frac{\sin h x}{e^x}$$

Limits and continuity

Analysis of the voltage in a hairdryer involves terms of the form$$\sin(nwt-90^{\circ})$$, where n is a positive integer, w is the frequency of the voltage, and t is time. Use an identity to simplify this expression.

Limits and continuity

Find the limit (if it exists) and discuss the continuity of the function. $$\displaystyle\lim_{{{\left({x},{y}\right)}→{\left({0},{0}\right)}}}{\frac{{{y}+{x}{e}^{{-{y}²}}}}{{{1}+{x}²}}}$$

Limits and continuity

Find the limit, if it exists. (If an answer does not exist, enter DNE.) $$\lim\arctan(e^{x})$$ $$x\approx\infty$$

Limits and continuity

Find the limit and discuss the continuity of the function. $$\displaystyle\lim_{{{x},{y}}}→{\left({0},{1}\right)}\frac{{\arccos{{\left(\frac{{x}}{{y}}\right)}}}}{{1}}+{x}{y}$$

Limits and continuity

Evaluate the following limits. $$\lim_{(x,y)\rightarrow(4,5)}\frac{\sqrt{x+y}-3}{x+y-9}$$

Limits and continuity

Find each of the following limits. If the limit is not finite, indicate or for one- or two-sided limits, as appropriate. $$\lim_{x\rightarrow\infty}\frac{4x^3-2x-1}{x^2-1}$$

Limits and continuity

Evaluate the following limits. $$\lim_{(x,y)\rightarrow(2,2)}\frac{y^2-4}{xy-2x}$$

Limits and continuity

Find the limits: $$\lim_{x\rightarrow-2}\frac{x+2}{\sqrt{x^2+5}-3}$$

Limits and continuity

Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy$$

Limits and continuity

Find the limits: $$\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}$$

Limits and continuity

Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(2,0)}\frac{1-\cos y}{xy^2}$$

Limits and continuity

Find the following limit: $$\lim_{x\rightarrow0}\frac{xe^x}{e^{3x}-1}$$

Limits and continuity

Evaluate the following limit. $$\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}$$

Limits and continuity