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rubik's user avatar
rubik
  • Member for 11 years, 11 months
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19 votes
Accepted

Integration substitution: How does Wolfram Alpha come up with this step?

16 votes
Accepted

If $A$ and $B$ are positive constants, show that $\frac{A}{x-1} + \frac{B}{x-2}$ has a solution on $(1,2)$

13 votes
Accepted

Show that 2n "1" digits subtract n "2" digits is a perfect square.

13 votes
Accepted

Showing the norm' is non-negative

12 votes
Accepted

Suppose that the sum of $11$ different natural numbers is $70$. How can I show that their product is divisible by $720$?

11 votes

Is $+15/3$ a natural number?

11 votes
Accepted

Proving that the roots of $1/(x + a_1) + 1/(x+a_2) + ... + 1/(x+a_n) = 1/x$ are all real

10 votes

Is there a trick to establish $z = \tan \left[ \frac{1}{i} \log \left( \sqrt{ \frac{1+iz}{1-iz} } \right) \right]$?

9 votes

Simplifying $\csc^{-1}(\sec 2)$?

9 votes
Accepted

Getting integer solutions for equation $x^{2}-y^{4}=336$

8 votes
Accepted

Evaluating $\lim_{x\rightarrow\pi}\frac{\sin x}{x^2-\pi ^2}$ without L'Hopital

7 votes
Accepted

Is $\tan^{-1}$ for $\arctan$ on my calculator wrong?

7 votes
Accepted

Solution of a integral

7 votes
Accepted

Limit problem: $\lim\limits_{n\to ∞} \sqrt[n]{7^n+3^n}$

7 votes
Accepted

Find $\lim_\limits{x\to 0}\left({\tan x\over x}\right)^{1\over 1-\cos x}$.

7 votes
Accepted

How to show the real part of a holomorphic function is harmonic

5 votes

Evaluating $\int_{0}^{\frac{\pi}{2}} (\sin (x) +\cos (x))^4 - (\sin(x) - \cos (x))^4 dx$

5 votes

Calculate a lim $\lim_{x\to \infty } \left ( \frac{x^2+2}{x^2-4} \right)^{9x^2} $

5 votes
Accepted

Evaluating the integral $\int_{-1}^1(5x^4-4x^3)\mathrm dx$

4 votes
Accepted

Computing $\int \sqrt{1+4x^2} \, dx$

4 votes

What is $\cdots ((((1/2)/(3/4))/((5/6)/(7/8)))/(((9/10)/(11/12))/((13/14)/(15/16))))/\cdots$?

4 votes

Find domain, $f(x) =\log(\log_{|\sin x|}(x^2-8x+23)-\large\frac{3}{\log_{2}|\sin x|})$

4 votes
Accepted

Counter example for $\lim \limits_{x \to a}g(f(x))$ = $g(\lim \limits_{x \to a}(f(x))$

4 votes
Accepted

Last two digits of $3^{7^{2016}}$

4 votes
Accepted

Which is correct: negative infinity or 'does not exist'?

4 votes
Accepted

Gamma function and Stirling's approximation

4 votes

How to evaluate $\sum_{k=1}^{\infty}{\frac{1}{(k+2)(k+3)}}$

3 votes
Accepted

Prove the limit of a piecewise function?

3 votes

Floor function: Maths Olympiad problem

3 votes
Accepted

Is there a way to check if a number is prime with only a few details about the number?

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