Step 1

\(\lim\arctan(e^{x})=\arctan(e^{\infty})\)

\(=\arctan(\infty)=\frac{\pi}{2}\)

\(\lim\arctan(e^{x})=\arctan(e^{\infty})\)

\(=\arctan(\infty)=\frac{\pi}{2}\)

asked 2021-05-16

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

asked 2021-06-28

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

asked 2021-06-07

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 \(\mu\)

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 \(\mu\)

asked 2021-05-28

Verify, using the definition of convergence of a sequence, that
the following sequences converge to the proposed limit.

a) \(\lim \frac{2n+1}{5n+4}=\frac{2}{5}\)

b) \(\lim \frac{2n^3}{n^3+3}=0\)

c) \(\lim \frac{\sin (n^2)}{\sqrt[3]{n}}\)

a) \(\lim \frac{2n+1}{5n+4}=\frac{2}{5}\)

b) \(\lim \frac{2n^3}{n^3+3}=0\)

c) \(\lim \frac{\sin (n^2)}{\sqrt[3]{n}}\)

asked 2021-05-28

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as \(\displaystyle{\left({x},{y}\right)}\rightarrow{\left({0},{0}\right)}.{f{{\left({x},{y}\right)}}}={e}^{{{x}{y}}}\)

asked 2021-05-27

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

asked 2021-05-01

\(\lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-z}\)

asked 2021-05-01

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

asked 2021-01-07

Let \(A=\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix} ,B=\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}\)

If possible , compute the following . If an answer does not exist , enter DNE.

AB,BA-?

True or False: AB=BA?

If possible , compute the following . If an answer does not exist , enter DNE.

AB,BA-?

True or False: AB=BA?

asked 2021-06-13