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Koro
  • Member for 6 years, 10 months
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11 votes
Accepted

Evaluating $\int\frac{e^{\tan^{-1} x}}{(1+x^2)^{\frac32}}dx$

7 votes
Accepted

Find the minimum of $\frac{\sin x}{\cos y}+\frac {\cos x}{\sin y}+\frac{\sin y}{\cos x}+\frac{\cos y}{\sin x}$

5 votes
Accepted

$\lim\limits_{x \to \infty} \frac{\ln x}{x} =0$

5 votes

Various ways to calculate $\int \sin(x) \cos(x) \, \mathrm{d}x$

5 votes
Accepted

How to find $\lim_{n\to \infty} \frac{\log(n)}{n}$ without L'Hospital's rule?

5 votes

Show that $\phi (x)\cdot \phi (y)=x\cdot y$ for all $x,y\in \mathbb{R}^3$

5 votes
Accepted

Is my proof for composition of uniformly continuous function correct?

5 votes

Arrangements of BANANAS where the A's are separated

5 votes

How do two conjugate elements of a group have the same order?

5 votes

How to prove that if $x>0$ and $y>0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$, using the relation of arithmetic and geometric means?

5 votes
Accepted

How to calculate $ \intop_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx $

4 votes

Proving that a function of the form f(x+y)=f(x)*f(y) is continuous

4 votes
Accepted

Spivak Calculus chapter 1 problem 13 proof critique

4 votes

$\int(x^{12}+x^8+x^4)(2x^8+3x^4+6)^{1/4}dx$

4 votes
Accepted

Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?

4 votes

Solving a simple rational equation $(\frac{6x}{6-x})^2+x^2=400$

4 votes
Accepted

Is there a difference between $(x)^{\frac{1}{n}} $ and $\sqrt[n]{x}$?

4 votes

Why this piecewise function doesn't have a removable discontinuity?

4 votes
Accepted

Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set

4 votes

Studying a series for convergence at the boundary points

4 votes
Accepted

Let be $c>0$ and $M>0$ such that $|a_nc^n|\leq M$. Prove that $(-c,c)$ is in the interval of convergence of the power series

4 votes

Prove that $\lim_{x \rightarrow +\infty} \frac{\text{log}(x+1)}{x} = 0$ without de l'Hopital rule

4 votes

True or False? If the limit of $[f(x)-g(x)]$ as x approaches $a = 0$, then the limit of $f(x), g(x)$, as $x$ approaches $a$, are equal.

4 votes

If $f$ has 3 zeros, then $\exists x_0: f''(x_0)=0$

4 votes

Prove that $f: \mathbb{R} \to \mathbb{R}, f(x) = x^\frac{1}{9}$ is not a differentiable function

4 votes
Accepted

Problem from Zorich's book volume 1

3 votes
Accepted

Show that $h$ is a constant.

3 votes
Accepted

Given that $3\sin x + 2\sin y = 4$. Find the maximum value of $3\cos x + 2\cos y$.

3 votes

How to go about finding whether this limit exists: $\lim_{x \to 0} x [[\frac{1}{x}]]$?

3 votes
Accepted

Trigonometric integral $\int^\pi_0\frac{d\theta}{1+a^2\sin^2\theta}$

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