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Sep
1
reviewed Close graph and equation
Sep
1
reviewed Close Find two numbers knowing their sum and their difference
Sep
1
reviewed Leave Open How many ways can a quadratic form represent a prime?
Sep
1
reviewed Leave Open Maximum of $xy^3z^7$ in the plane $x+y+z=1$
Aug
21
comment In the real domain, are there any theorems or definitions that state all functions are differentiable?
"the most famous mathematicians who lived two centuries ago did believe that every function had a derivative." This is a bit strange. Maybe "was differentiable almost everywhere" would be better? I'm thinking about examples like $f(x) = |x|$, as I don't know whether they were thought as functions back then.
Aug
2
awarded  Great Question
Jul
23
comment Using a visual “proof” to show that $\sum_{n=1}^{\infty} \left(\frac 34 \right)^n =1$
And $\sum_0^\infty (3/4)^k = 4$, right?
Jul
15
comment If $\lim\limits_{n \to \infty} \frac{a_n}{b_n}=1 \rightarrow \sum_{n=1}^\infty a_n = \sum_{n=1}^\infty b_n$
Try to change just, say, $a_1$...
Jul
13
comment Does the series $∑\frac {8n}{(\log n)^n}$ converge or diverge?
$2<\log (n)$ from some point on.
Mar
6
comment Linear transformations such that $A^3=I$ but $A^2\neq I$
Consider rotating a plane by $120^\circ$.
Mar
5
answered Proof with derivatives (most likely induction)
Mar
4
awarded  Popular Question
Mar
3
comment An attempt at an epsilon-delta proof of the fundamental theorem of calculus
"...we know that $\exists \delta >0$ such that for any $\varepsilon >0$..." You mean the contrary logical order: for any $\varepsilon$ there is a $\delta$. That said, can you show that $\lim_\limits{h\to 0^+} (F(x+h)-F(x))/h=\lim_\limits{h\to 0^-}(F(x+h)-F(x))/h=f(x)$ implies $\lim_\limits{h\to 0}(F(x+h)-F(x))/h=f(x)$?
Mar
3
comment Differentiable $N$ times, $f'(x_{0})=\cdots=f^{(N-1)}(x_0)=0$, $f^{(N)}(x_0)>0\implies f$ increasing on $x_0$?
The remainder is usually written $r_n(h)$ with $\lim_\limits{h\to 0}r_n(h)/h^n = 0$; here I wrote $\rho(h) = r_n(h)/h^n$ with $\lim_\limits{h\to 0} \rho(h) =0$ and simplified the expansion for our analysis.
Mar
3
revised Differentiable $N$ times, $f'(x_{0})=\cdots=f^{(N-1)}(x_0)=0$, $f^{(N)}(x_0)>0\implies f$ increasing on $x_0$?
added 16 characters in body
Mar
3
answered Differentiable $N$ times, $f'(x_{0})=\cdots=f^{(N-1)}(x_0)=0$, $f^{(N)}(x_0)>0\implies f$ increasing on $x_0$?
Feb
18
comment Prove that $a_1^2+a_2^2+\dots+a_n^2\ge\frac14\left(1+\frac12+\dots+\frac1n\right)$
"(...) which means that $a_k\geq \sqrt{k}-\sqrt{k-1}.$" I don't follow, is the sum bounded above by something?
Feb
8
comment supremum and infimum: $\frac{n^n}{n!^2}$
This is off by a factor of $n+1$ ($a_{n+1}$ is $(n+1)^{n+1}/(n+1)!^2$, not $(n+1)^{n}/(n+1)!^2$). Of course, the answer is correct despite this.
Feb
8
comment supremum and infimum: $\frac{n^n}{n!^2}$
You will find the ratio $a_{n+1}/a_n$ very interesting. Use it to show that $a_{n+1}/a_n <1/2$ from some point on.
Jan
21
answered If $3^x$ and $5^x$ are both integers, is $x$ an integer?