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hamam_Abdallah
  • Member for 7 years, 7 months
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  • Meknès-Morocco
11 votes
6 answers
719 views

Without using approximation, prove that $ \ln(4)<\sqrt{2}$.

7 votes
1 answer
834 views

Proving $\sum_{i=1}^n\sum_{j=1}^n\sqrt{|x_i-x_j|}\le \sum_{i=1}^n\sum_{j=1}^n\sqrt{|x_i+x_j|}$.

5 votes
2 answers
72 views

Prove that the curve of the function $ f $ has an asymptote near infinity which is parallel to the line $ y=x $

5 votes
2 answers
383 views

How to compute $\int_0^{\frac{\pi}{2}}\frac{\arctan(\sqrt{\tan(x)})}{\tan(x)}dx$

5 votes
1 answer
204 views

Prove if $\lim_{x\to +\infty}(f(x)+f'(x))=0$ then $\lim_{x\to +\infty} f(x)=0$ [duplicate]

4 votes
2 answers
86 views

Is it possible to compute $\int_0^x\frac{t^2dt}{(t\sin(t)+\cos(t))^2}$?

4 votes
1 answer
58 views

Is it possible to find the expression of the antiderivative $\int \frac{dx}{\cosh(x)+\sqrt{\cosh(2x)}}$

4 votes
2 answers
94 views

find the limit of the sum $\sum_{k=n}^{2n-1}\frac{1}{2k+1}$

4 votes
0 answers
100 views

How to draw the segment $[A,B] $ with only a ruler whose length is too short.

3 votes
3 answers
449 views

Find function $ f $ such that $f(\frac{x-3}{x+1})+f(\frac{x+3}{1-x})=x$

3 votes
2 answers
226 views

How to show this inequality $ a^{14}-a^{13}+a^8-a^5+a^2-a+1>0$

3 votes
1 answer
70 views

Prove that some subsets contain two positive integers $ a $ and $ b $ such that $ a|b$

3 votes
1 answer
113 views

No rational has a square of the form $\frac 1t-t$ where $ t $ is a rational in $(0,1)$

3 votes
1 answer
62 views

Limit of a nearly Riemann sum

3 votes
3 answers
823 views

Could the set of fixed points be uncountable?

3 votes
3 answers
258 views

Prove an equality with floor function.

2 votes
1 answer
75 views

Is it possible to compute $\int_e^{e^2}\frac{e^xdx}{x\ln(x)}$

2 votes
1 answer
40 views

Compute the integral $\int_0^\pi \frac{\ln(1+\cos(t))}{\cos(t)}dt$ using a double integral.

2 votes
4 answers
92 views

Prove that if $\sum_{i=1}^n\lambda_i|x-a_i|=0$ then $\lambda_1=\lambda_2=\cdots \lambda_n=0$ [closed]

2 votes
1 answer
63 views

Prove that the function $ g $ satisfying $g(g(x))=2g(x)-x $ is strictly monotonic.

2 votes
3 answers
70 views

Can we say that $\forall x\in \Bbb R$, $g(x)>0$, $g(x)<0 $ or that $(\exists x\in \Bbb R) g(x)=0$.

1 vote
2 answers
107 views

Find all positive integers $ a $ and $ b $ such that $7^a-3(2^b)=1$ [closed]

1 vote
1 answer
38 views

What is the domain of the function $ f:x\mapsto \int_0^1\frac{t^x-1}{\ln(t)}dt$

1 vote
2 answers
164 views

Without computing it, conclude that $\tan(\frac{\pi}{8})$ is irrational. [closed]

1 vote
1 answer
34 views

Prove an identity for a special sequence with 1 and 2.

1 vote
0 answers
58 views

Are there other methods to prove this inequality?

1 vote
1 answer
56 views

What is the fastest way to compute the limit $\lim_{x\to 0^+}x\cosh^{-1}(x\sinh(\frac 1x))$

1 vote
2 answers
403 views

How to join two points with only a small ruler. [duplicate]

1 vote
1 answer
147 views

Prove the next cyclic inequality

1 vote
3 answers
157 views

Is there a direct proof of the inequality $cyclic \sum\frac {a^2+1}{b+c}\ge 3$