Clement Yung's user avatar
Clement Yung's user avatar
Clement Yung's user avatar
Clement Yung
  • Member for 5 years, 4 months
  • Last seen this week
15 votes
Accepted

Proving that $f'(x)\le f(x), \forall x\in \mathbb{R}$

9 votes
Accepted

$\int_0^1f(x) dx =0$, $\int_0^1xf(x) dx =0$. How to show that f has at least two zeros?

7 votes
Accepted

Let $a$ and $b$ be elements of odd order in a finite group. Show that $a^2$ and $b^2$ commute if and only if $a$ and $b$ commute.

7 votes
Accepted

Why does Stolz- Cesaro fail to evaluate the limit of $\dfrac{n + n^2 + n^3 + n^4 + \ldots + n^n}{1^n + 2^n + 3^n + 4^n + \ldots +n^n}$,

7 votes

Proving that the set of rational numbers between 0 and 1 is disconnected.

7 votes
Accepted

In which case these integrals are equal?

7 votes
Accepted

How can I turn a $0^0$ form into a $\frac{\infty}{\infty}$ or $\frac{0}{0}$ form?

6 votes
Accepted

show that $x_1^2+x_2^2+\cdots+x_{2020}^2\geqslant x_1x_2+x_2x_3+\cdots+x_{2020}x_1$

6 votes
Accepted

Find $a_n:a_{n+1}$ if $a_n=\int_0^{\pi/2}\cos^nx.\cos nx.dx$

6 votes
Accepted

Differentiability of $\cos \lvert x\rvert$

6 votes
Accepted

If you divide two equations by each other and you get a valid equation, does that necessarily mean original equations are also valid?

6 votes
Accepted

The definition of cofinality of an ordinal

6 votes

In what sense are proofs that rely on the Law of the Excluded Middle really proofs?

5 votes
Accepted

What is the superior limit of this sequence?

5 votes
Accepted

Convergence of a particular infinite series

5 votes
Accepted

what is $\sum_{n=1}^\infty\frac{1}{n!\log n!}$

5 votes
Accepted

Find the Maxima of $g(x)= xe^{x^{2}} + e^{-x^{2}}$ in $[0,1]$

5 votes

Prove the surjectivity of $f(r,m)$ from $\mathbb{Z^{+}} \times \mathbb{N} \rightarrow 2\mathbb{N}+1$

4 votes
Accepted

Explain why $\arccos(t)=\arcsin(\sqrt{{1}-{t^2}})$ when $0<t≤1$.

4 votes
Accepted

Prove:$\lim_{x\to \infty}\frac{\lfloor 3e^x\rfloor+2}{\lfloor 2e^x\rfloor+1}=\frac{3}{2}$

4 votes

Inequality $\frac{x^3}{x^2+y^2}+\frac{y^3}{y^2+z^2}+\frac{z^3}{z^2+x^2} \geqslant \frac{x+y+z}{2}$

4 votes
Accepted

Bounded and finite stopping times

4 votes
Accepted

If $p(x) = ax^3 + bx^2+cx+105$, $a+b+c=0$, $a,b,c \in \mathbb{Z}$ then $f(x)=0$ having no roots $\in \mathbb{Z}$

4 votes
Accepted

How should I solve the equation $\sqrt{x-\frac 1x}+\sqrt{1-\frac 1x}=x$

4 votes
Accepted

Prove that$\frac{1}{(x+1)^2+y^2+1}+\frac{1}{(y+1)^2+z^2+1}+\frac{1}{(z+1)^2+x^2+1}\le\frac{1}{2}$

4 votes
Accepted

Is $1.r=r.1=r$ for a Non Commutative Ring

4 votes
Accepted

Why is $f(x+h) = 3x+3h-1$ when $f(x)=3x-1$?

4 votes
Accepted

A simple inequality involving product xyz and xy

4 votes
Accepted

Derivative of Integral (Fundamental Theorem of Calculus)

4 votes
Accepted

Decreasing sequence term sign for zero convergent series

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