Wang YeFei's user avatar
Wang YeFei's user avatar
Wang YeFei's user avatar
Wang YeFei
  • Member for 2 years, 6 months
  • Last seen this week
  • Chengdu, Sichuan, China
10 votes

What is maximum value of $f(t)=16\cos t \cdot \cos 2t \cdot\cos 3t \cdot \cos6t$

7 votes

How to show that $\left(\sqrt{\binom{n}{1}}+\sqrt{\binom{n}{2}}+...+\sqrt{\binom{n}{n}}\right)^2≤n(2^n-1)$?

7 votes
Accepted

show that there is no a positive integer $n$ for which $\sqrt{n+1} + \sqrt{n-1}$ is rational

7 votes
Accepted

Integral inequality, proof verification

7 votes
Accepted

Are the positive irrational numbers closed under addition?

6 votes

Prove that if $\lim_{x \to +\infty} f(x)=0$ and $f(x) \ge 0$ $\forall x \ge 0$, then $\int_{0}^{+\infty}f(x)dx$ is finite.

6 votes

How to Find the Limit Correctly?

5 votes

Deriving $\operatorname{arccot}(x)=\int\limits_{x}^ {\infty} \frac{1}{1+t^2} ~dt$

5 votes
Accepted

Find a side using similarity of triangles

5 votes

Maximizing/minimizing $f(\theta) = \sqrt{2}\cos(\theta)-4\sin(\theta)$

5 votes

Prove a limit equals to $0$

5 votes

Is $∃!x(x^2 = 1)$ true?

5 votes
Accepted

Limit at (0,0) of $\frac{xy^2\sqrt{x^2+y^2}}{x^2 +y^4}$

4 votes
Accepted

Finding $ \lim_{x\to0}\frac{(\sin x^2)^3 - (\sin x^3)^2}{\ln(1+x^{10} )}$

4 votes
Accepted

$|a|−|b|$ is less than or equal to $|a−b|$

4 votes

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

4 votes
Accepted

$3\times 2^m + 4 = n^2$

4 votes

If $a^{2}+b^{2} \leq 4$, prove that $a+b \leq 4$

4 votes
Accepted

How many vectors are there in the basis of solution set for Ax=0?

4 votes

Find minimum $|z|$ satisfying $|z + 1/z |= 2$.

4 votes
Accepted

Finding the minimum value of $(x_1-x_2)^2 +\left(\frac{9}{x_1} - \sqrt{1-x_2^2}\right)^2$ by using trigonometry

4 votes
Accepted

find the minimum of $A=\frac{x^3}{3y+1}+\frac{y^3}{3z+1}+\frac{z^3}{3x+1}$ with $x^3+y^3+z^3=3$

4 votes
Accepted

Evaluating integral of the form $\int \frac {dx}{(x-b)^m(x-a)^n}$

4 votes

Find the maximum of $\frac{abc}{(4a+1)(9a+b)(4b+c)(9c+1)}$,where$a,b,c>0$

4 votes
Accepted

Proving $4 \nmid n^2+2$ for all $n \in \mathbb{Z}$

4 votes
Accepted

How to prove that $\sqrt{\frac{x^2+1}{x+1}}+\frac{2}{\sqrt{x}+1}\ge2, \text{ }x\in \mathbb{R}_{>0}$?

4 votes
Accepted

Let $a,b,c>0$ and $ab+bc+ca=3$. Prove that $abc(a+b)(b+c)(c+a)\leq8$

4 votes

Mean Value Theorem applied to exponential function

4 votes
Accepted

Find the measure of the smallest positive angle $\theta$ in degrees for which $\tan\theta=\frac{\cos25^\circ+\cos85^\circ}{\sin25^\circ-\sin85^\circ}$

4 votes
Accepted

Limit with non square roots without l'Hôpital’s rule

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