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Nicolas FRANCOIS
  • Member for 6 years, 7 months
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16 votes
Accepted

Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$

9 votes

Why does $\ker(T) = \{0\} \Leftrightarrow T$ is injective

7 votes
Accepted

How to prove that $\int_{-\infty}^{\infty}f'(t)\exp(-t^2)\text{d}t$ is finite when $\lim_{|t|\to \infty}f(t)\exp(-t^2) = 0$?

6 votes

Induction differential proof

6 votes

Find $f(1)+\cdots+f(60)$

5 votes
Accepted

Condition for the roots of $x^n+a_1x^{n-1}+a_2x^{n-2}+\ldots+a_n=0$ not all to be real

5 votes
Accepted

How to find the value of $\lim_\limits{x \to 0}\frac{e^{x\cos{x^2}}-e^{x}}{x^5}$

5 votes

Show that $\log(x+1)-\log(x)<\frac{1}{x}$ for $x >0$

5 votes

Question about continuous function.

5 votes
Accepted

How to sum: $\sum_{n=0}^{\infty} (n^2+2n+1)·(2·\ln(x))^n$

4 votes
Accepted

Proving integral $\int_0^1\frac{e^x-1}{x}$ is equal to $\sum_{n=1}^{\infty}\frac{1}{n \cdot n!}$

4 votes

Showing that the only roots of a ploynomial are $x=0, y=0$

4 votes
Accepted

Dice rolling / Smallest value probability

4 votes
Accepted

For an element with infinite order, how many generators does $\left \langle a \right \rangle$ have

4 votes

divergence rate of $\sum_{n=1}^k\frac{1}{1+n\log n}$

4 votes

What are all the isomorphisms from $\mathbb{K}[x] \to \mathbb{K}[x]$?

4 votes
Accepted

Finding $\lim_{n \to \infty} \prod_{r=1}^n (1+ \frac{1}{a_r})$

4 votes

Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $

4 votes
Accepted

Why $\int_0^\infty \sin^2(x)/x^2 dx$ converges, and $\int_0^\infty \cos^2(x)/x^2 dx$ does not?

4 votes
Accepted

how to solve tan(pi(cot(x))) = cot(pi(tan(x)))

3 votes

Multivariable limit - perhaps a trickier problem I am stuck on.

3 votes

Prove that the function is continuous at $ x=1$

3 votes
Accepted

Convergence of $u_{n+1} =\sqrt{\sum_{k=0}^{n} u_k}$

3 votes

How to solve $\lim_{(x,y)\to(0,0)}\frac{x^{3}}{x^{2}+y^{2}}$?

3 votes
Accepted

Squeezing to find a limit

3 votes

Inverse function to $f(x)=\frac{e^x-e^{-x}}{2}$

3 votes
Accepted

If $A,B,C$ commute, then they are mutually diagonalizable

3 votes

What is the probability that the special ball is chosen?

3 votes

Proof that convergent sequence in $\Bbb R$ is bounded.

3 votes
Accepted

Show that $z\in\mathbb{C}$ satisfying $\arg\Big(\dfrac{z-1}{z+1}\Big)=\dfrac{\pi}{4}$ is a circle

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