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Pierpaolo Vivo's user avatar
Pierpaolo Vivo's user avatar
Pierpaolo Vivo's user avatar
Pierpaolo Vivo
  • Member for 8 years, 5 months
  • Last seen more than 2 years ago
24 votes
Accepted

How to solve this equation manually: $(x^2+100)^2=(x^3-100)^3$?

15 votes
Accepted

Solving for the CDF of the Geometric Probability Distribution

12 votes
Accepted

Proof of value of infinite series, using definition of the integral

11 votes
Accepted

Writing $1/(X+i\epsilon)$ in terms of principal value and imaginary part

11 votes
Accepted

Prove that $f'(1)=0$ if $f(x^2)-\sin f(x)=1$

7 votes
Accepted

Evaluate $\sum_{r=1}^{\infty} \frac{\sin(r\pi x)}{r \cdot y^r}$

7 votes
Accepted

Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?

6 votes

Evaluating $\lim_{x \to 0}{\frac{\sin(4x)}{\sin(3x)}}$ without L'Hospital

6 votes
Accepted

Creative way for $\int _0 ^1 \frac{x^4 (1-x)^4} {x^2 +1} {\rm d}x$

6 votes

Closed form for $\int_0^1...\int_0^1\frac{1}{\left(1+\sqrt{1+x_1^2+...+x_n^2}\right)^{n+1}}\;dx_1...dx_n$

5 votes
Accepted

Find $\lim_{x\to0}|x|^{\sin x}$

5 votes
Accepted

Integrate exponential over shifted square root

5 votes

Evaluate $\lim \limits_{n\to\infty} ne^{-nx^2}$

5 votes

For which values of real a does the following matrix have an inverse?

5 votes
Accepted

Cauchy Principal value of integral with undefined point

5 votes
Accepted

Has this summation a specific result?

4 votes
Accepted

Calculate an approximation of $\int_0^1\int_0^1\frac{\log(xy)xy}{-1+\log(xy)}dxdy$

4 votes

Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?

4 votes

Solve the limit $\lim _{x\to \infty \:}\left(\frac{\left(\left(2x\right)!\right)}{x^xx!}\right)^{\frac{1}{x}}$

4 votes

(Non)Existence of limits

4 votes

Find the sum $\sum _{ k=1 }^{ 100 }{ \frac { k\cdot k! }{ { 100 }^{ k } } } \binom{100}{k}$

4 votes

Compute the given limit as $x$ approaches $\infty$

3 votes
Accepted

Asymptotic distribution of ratio of two coordinates of random unit-vector

3 votes
Accepted

Dirac Delta of a Function When the Derivative of the Function is Discontinuous at its Roots

3 votes
Accepted

Finding $\lim_{x\to \infty}(1+\frac{2}{x}+\frac{3}{x^2})^{7x}$

3 votes

Explicit Formula for Multiple Integral

3 votes

Find $\lim_{n\to\infty} \frac{(n!)^{1/n}}{n}$.

3 votes
Accepted

Expected value of $1/X$.

3 votes
Accepted

Find $x = \log_2(4^{3\over 4}\cdot \sqrt{2^5})^{1 \over 2}$

3 votes
Accepted

Domain of logarithmic function

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