TenaliRaman's user avatar
TenaliRaman's user avatar
TenaliRaman's user avatar
TenaliRaman
  • Member for 11 years, 10 months
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22 votes

What does a space mean?

22 votes
Accepted

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

22 votes

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

17 votes
Accepted

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

16 votes

What is a good book to study linear algebra?

11 votes
Accepted

Why do we use gradient descent in the backpropagation algorithm?

10 votes

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

10 votes

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

8 votes
Accepted

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

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}$

7 votes
Accepted

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

6 votes
Accepted

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

6 votes
Accepted

how do you learn trigonometric identities

6 votes

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

6 votes
Accepted

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

5 votes
Accepted

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

5 votes
Accepted

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

5 votes

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

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!}+...$

5 votes
Accepted

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

4 votes
Accepted

Prove convexity of set with triangular inequality

4 votes

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

4 votes

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

4 votes
Accepted

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

4 votes
Accepted

Unbiased estimator for $\theta$

4 votes

What is the intuition for using definiteness to compare matrices?

4 votes
Accepted

Sampling a Gaussian in a Bayesian network

4 votes

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

3 votes
Accepted

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

3 votes

How to prove such an elementary inequality