Chris's wise sister

less info
meta site favicon meta user | stack exchange network profile network profile
11,517 reputation
11373
bio website
location
age
visits member for 1 year
seen 7 mins ago
stats profile views 3,643

Your beloved sister ;)


206 Answers

newest activity votes
31
The last digit of $2^{2006}$
13
How to integrate $\int_1^e \ln{x} \, dx$
11
Prove $\int_0^1 \frac{t^2-1}{(t^2+1)\ln t}dt = 2\log\left( \frac{2\Gamma \left( \frac{5}{4}\right)}{\Gamma\left( \frac{3}{4}\right)}\right)$
11
Inequality $a+b+c \geqslant abc +2$
10
Prove the following identity
10
Evaluating $ \int_0^{\pi/2}\frac{(\ln{\sin x})(\ln{\cos x})}{\tan x}dx $
7
$\displaystyle\lim_{n\to \infty} n^2(\sqrt[n]{2}-\sqrt[n+1]{2})$
7
Calculate $\ln(2)$ using Riemann sum.
6
How to find the last digit of $37^{100}$
6
Evaluate the limit $\lim_{n\to\infty}\left[n+{n^2}\log{\frac{n}{n+1}}\right]$
6
Proving $\int_{0}^{+\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$
6
Inequality. $a^2+b^2+c^2 \geq a+b+c$
6
Evaluating $ \int_1^{\infty} \frac{\{t\} (\{t\} - 1)}{t^2} dt$
5
Proving $x^x+y^y\ge\sqrt2$ when $x,y\in \mathbb R^+$ and $x+y=1$
5
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
5
How do I evaluate the limit $\lim_{n\to\infty}n((1+1/n)^n-e)$?
5
Faster way to compute the integral
5
Verifing $\int_0^{\pi}x\ln(\sin x)\,dx=-\ln(2){\pi}^2/2$
5
Show $ \int_0^\infty\left(1-x\sin\frac 1 x\right)dx = \frac\pi 4 $
5
Evaluate $\lim_{n \to \infty }\frac{(n!)^{1/n}}{n}$.
5
Limit of $\sqrt[n]{a^n-b^n}$ as $n\to\infty$
4
Please how to find indefinite integral $\int x^{x^x}\mathrm dx$?
4
How can we show the convergence of $x_n = \sin(2\pi (n^3-n^2+1)^{\frac{1}{3}})$?
4
I need assistance in integrating $ \frac{x \sin x}{1+(\cos x)^2}$
4
Suppose $(a_n)$ is a sequence such that $a_n=\frac{1!+2!+\cdots+n!}{n!}$. Show that $\lim{a_n}=1$
4
Find $\lim_{x\to 0^+} \ln x\cdot \ln(1-x)$
4
$\int_0^{\infty}\frac{\ln x}{x^2+a^2}\mathrm{d}x$ Evaluate Integral
4
Finding $\int^1_0 \frac{\log(1+x)}{x}dx$ without series expansion
4
How can I find $\lim_{n \to \infty}[(1-\frac{1}{2^2})(1-\frac{1}{3^2})\cdots(1-\frac{1}{n^2})]$
4
Another simple series convergence question
1 2 3 4 5 … 7