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Atmos's user avatar
Atmos's user avatar
Atmos
  • Member for 6 years, 3 months
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20 votes

Is a Lipschitz function differentiable?

10 votes

What can using the "opposite" combination for integration by parts be used for

8 votes
Accepted

Find $\int_{\frac{1}{e}}^{e}|\ln x| dx$

8 votes
Accepted

Is this sequence convergent for n in natural numbers

8 votes
Accepted

Prove $\int_{\pi}^{\infty}\frac{\cos(x)}{x}dx$ is convergent

7 votes
Accepted

How to simplify this formula: $ x^{\ln \left( 3 \right)}-3^{\ln \left( x \right)}$?

6 votes

What is the largest eigenvalue of the following matrix?

6 votes
Accepted

Find the value of the expression: $\frac{1}{\sqrt{4}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{10}}+\cdots+\frac{1}{\sqrt{13}+\sqrt{16}}$

6 votes

Proof of this integration shortcut: $\int_a^b \frac{dx}{\sqrt{(x-a)(b-x)}}=\pi$

6 votes
Accepted

Complex Trigonometric Integration using Residue formula

5 votes

Integral $\int_0^{\pi} \frac{\cos(2018x)}{5-4\cos{x}}dx$

5 votes

Evaluation of $\lim_{n \to \infty} \int_{0}^\infty \frac{1}{1+x^n} dx$

5 votes

How to show $\int_{0}^{\infty} \frac{dx}{x^3+1} = \frac{2\pi}{3\sqrt{3}}$

5 votes
Accepted

Problem with recurrence relation splitting into two.

5 votes

Continuous $f$ such that $f(x)=f(x^2)$ is constant?

4 votes
Accepted

Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$

4 votes
Accepted

How can I find $x(t)$?

4 votes
Accepted

Evaluate $\lim_{(x,y)\to (0,0)}\frac{x+\sin y}{x+y}$

4 votes

Integration with reciprocal

4 votes
Accepted

absolute value definition.

4 votes

Calculate $\lim_{n\to \infty}(n+1)^{\frac{1}{\sqrt{n}}}$

4 votes

How do I determine this integral? $\int_{0}^{+\infty}\sin^2(1/x)\frac{dx}{(4+x^2)^2}$

4 votes

Proving the determinant of this matrix is $0$: $\left(\begin{smallmatrix}2&1&0&5\\-1&1&1&6\\5&1&-1&4\\5&1&3&0\end{smallmatrix}\right)$

4 votes

why integration of $y=\frac{1}{1+x^2}$ is $\arctan(x)+c$?

3 votes
Accepted

then find the the radius of convergence of the following power series $\sum_{n=1} ^{\infty}a_nx^n$ about $ x =0$?

3 votes

Prove the Taylor series for $f(x)=\sqrt{x+1}$ of $f$ about zero converges to $f$ for all $x$ in $(0,1)$.

3 votes
Accepted

General term for fibonacci sequence

3 votes
Accepted

Euler integral - beta function

3 votes
Accepted

Evaluate $f(\pi^2)$, $f(-\pi^2)$

3 votes
Accepted

How to prove that $\lim\limits_{n\to\infty}\left(1+\frac{1}{p_n}\right)^{p_n}=e$?

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