User TenaliRaman

22 votes

What does a space mean?

answered Apr 23, 2012 at 21:41

22 votes

Accepted

What is the simplest proof that the mutual information $I(X:Y)$ is always non-negative?

answered Jun 17, 2012 at 16:55

22 votes

$\int_{0}^{\infty} \frac{e^{-x} \sin(x)}{x} dx$ Evaluate Integral

answered Jun 18, 2012 at 10:41

16 votes

What is a good book to study linear algebra?

answered Jun 19, 2012 at 12:36

16 votes

Accepted

show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$

answered Jul 27, 2013 at 4:08

11 votes

Accepted

Why do we use gradient descent in the backpropagation algorithm?

answered Mar 27, 2013 at 10:09

10 votes

Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$

answered Mar 8, 2013 at 4:23

10 votes

Calculate: $\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$

answered Jun 20, 2012 at 11:28

8 votes

Accepted

What does it mean to restricting a function to a line in convex optimization?

answered Feb 2, 2013 at 9:40

7 votes

Sum the series: $ S = \frac{1}{2} \cdot \sin\alpha + \frac{1\cdot 3}{2 \cdot 4} \sin{2\alpha} + \cdots \ \text{ad inf}$

answered Apr 23, 2012 at 10:02

6 votes

Accepted

Integral of $\int 2\,\sin^{2}{x}\cos{x}\,dx$

answered Jun 15, 2012 at 19:54

6 votes

Accepted

how do you learn trigonometric identities

answered Jan 6, 2013 at 10:44

6 votes

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

answered Feb 13, 2015 at 4:29

6 votes

Accepted

Evaluating $\int_0^{\pi/2} \frac{a}{a^2+\cos^2 \theta} \, d\theta$

answered Mar 11, 2015 at 11:34

6 votes

Accepted

Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$

answered May 15, 2018 at 17:26

5 votes

Accepted

Find the sum of the infinite series: $ 1 + \frac{1+2}{2!} + \frac{1+2+2^2}{3!} +\frac{1+2+2^2+2^3}{4!}+...$

answered Feb 11, 2017 at 3:43

5 votes

Accepted

Is it true that $(PQ+I)^{-1}P = P(QP+I)^{-1}$?

answered Feb 11, 2019 at 18:20

5 votes

Accepted

Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$

answered Feb 1, 2016 at 23:57

5 votes

Accepted

how to show $\frac{1+\cos x+\sin x}{1+\cos x-\sin x} = \frac{1+\sin x}{\cos x}$

answered Mar 11, 2015 at 9:40

5 votes

Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$

answered Jul 7, 2012 at 21:09

4 votes

What is the intuition for using definiteness to compare matrices?

answered Nov 17, 2012 at 12:08

4 votes

Accepted

Sampling a Gaussian in a Bayesian network

answered May 28, 2012 at 8:30

4 votes

Prove $(1 +\frac{ 1}{n}) ^ {n} \ge 2$

answered Mar 11, 2015 at 2:39

4 votes

Accepted

Prove convexity of set with triangular inequality

answered Feb 22, 2019 at 15:00

4 votes

Prove that $\sin\frac{\pi}n·\sin\frac{2\pi}n···\sin\frac{(n-1)\pi}n=\frac{n}{2^{n-1}}$

answered Feb 11, 2017 at 4:46

4 votes

Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{1}{4\cos^{2}x + 9\sin^{2}x} dx$

answered Mar 26, 2016 at 5:24

4 votes

Accepted

Solve for $x$ using the lambert W function $ \frac{\ln(1+bx)}{x} = a$

answered Mar 27, 2016 at 3:52

4 votes

Accepted

Unbiased estimator for $\theta$

answered May 27, 2018 at 7:31

3 votes

Accepted

$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$

answered May 14, 2014 at 13:16

3 votes

How to prove such an elementary inequality

answered May 16, 2014 at 22:17

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95 Answers

What does a space mean?

What is the simplest proof that the mutual information $I(X:Y)$ is always non-negative?

$\int_{0}^{\infty} \frac{e^{-x} \sin(x)}{x} dx$ Evaluate Integral

What is a good book to study linear algebra?

show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$

Why do we use gradient descent in the backpropagation algorithm?

Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$

Calculate: $\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$

What does it mean to restricting a function to a line in convex optimization?

Sum the series: $ S = \frac{1}{2} \cdot \sin\alpha + \frac{1\cdot 3}{2 \cdot 4} \sin{2\alpha} + \cdots \ \text{ad inf}$

Integral of $\int 2\,\sin^{2}{x}\cos{x}\,dx$

how do you learn trigonometric identities

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

Evaluating $\int_0^{\pi/2} \frac{a}{a^2+\cos^2 \theta} \, d\theta$

Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$

Find the sum of the infinite series: $ 1 + \frac{1+2}{2!} + \frac{1+2+2^2}{3!} +\frac{1+2+2^2+2^3}{4!}+...$

Is it true that $(PQ+I)^{-1}P = P(QP+I)^{-1}$?

Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$

how to show $\frac{1+\cos x+\sin x}{1+\cos x-\sin x} = \frac{1+\sin x}{\cos x}$

Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$

What is the intuition for using definiteness to compare matrices?

Sampling a Gaussian in a Bayesian network

Prove $(1 +\frac{ 1}{n}) ^ {n} \ge 2$

Prove convexity of set with triangular inequality

Prove that $\sin\frac{\pi}n·\sin\frac{2\pi}n···\sin\frac{(n-1)\pi}n=\frac{n}{2^{n-1}}$

Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{1}{4\cos^{2}x + 9\sin^{2}x} dx$

Solve for $x$ using the lambert W function $ \frac{\ln(1+bx)}{x} = a$

Unbiased estimator for $\theta$

$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$

How to prove such an elementary inequality