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Apr
15
comment Calculating exponential limit
First of all What have you tried thus far and why do you think you know the result? and furthermore did you mix up $n$ and $x$ variables? What is $x$?
Apr
1
comment Simplify $(n+1)^{1/\sqrt{n}}$ and $(n^2+1)^{1/n}$
Yeah I was considering $\sqrt[n]{n}\to 1$ as well but couldn't really compare the sequences to this root.
Mar
30
comment Issues computing $\int\cos^2x~\mathrm{d}x$ without using $\sin^2(x)=1-\cos^2(x)$
I know that I am going round and round but I was curious whether there is a more thorough explanation why besides $(\cos x)''=-\cos x$.
Mar
29
comment Issues computing $\int\cos^2x~\mathrm{d}x$ without using $\sin^2(x)=1-\cos^2(x)$
@YuriyS Chosing between $\sin x$ and $\sin x$ can yields different results - it the same :P
Mar
26
comment Prove the series $\sum_{n=1}^∞ (-1)^n(n)/(n+2)$ diverges
@Garrett $$\frac{n}{n+2}=\frac{1}{1+2/n}\overset{n\to\infty}{\longrightarrow}1\neq 0$$
Feb
12
comment Deducing the series expansion of $\arctan(x^2)$ via the series expansion of $\arctan(x)$ at $x=0$
So we must show that the replacement still yields a valid power series and that it has the same radius of convergence?
Jan
27
comment Multivariable taylor series expansion of $\exp(-(x^2+y^2))$
Am I right in assuming that $-\exp(-5)(4x+2y-11)$ would be the right polynomial in my case?
Jan
21
comment Eigenvectors of $\begin{pmatrix}6&2\\-10&-1\end{pmatrix}$ (linear equations with complex numbers)
@Prospect I do know the algorithm but I am struggling with the particular steps in this specific case.
Dec
9
comment Continuous function taking each of its values twice
It seems I am misunderstanding something in regards to the claim from the paper as all examples that come to mind have a finite amount of discontinuities.
Dec
9
comment Continuous function taking each of its values twice
Every function that satisfies this property has an infinite number of discontinuities. Refer to ams.org/journals/proc/1986-098-02/S0002-9939-1986-0854049-8/…
Dec
9
comment Using L Hopital's Rule Using $e$
$e=\exp(1) \rightarrow (\exp(1))'=(1)'\cdot\exp(1)=0$ as AndreasT mentioned.
Dec
8
comment Definite integral $\int _{0}^{1}\sqrt [3] {2x^{3}-3x^{2}-x+1}~\mathrm dx$
What have you tried so far?
Dec
7
comment Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$
Could you please elaborate why the term $[-\ln(x)/(\mu x^\mu)|_1^M$ remains finite as $M\to\infty$?
Dec
2
comment Trying to understand some terminology
Short version: $\mathcal{O}(n)$ is the class of functions which behave asymptotically similiar to $f(n)=n$. You would say that a function is in $\mathcal{O}(n)$ if it does not grow much faster than $n$. Examples would be $2n, 14n,\ldots$. Refer to this article for more detailed information about Big O notation.
Dec
1
comment How does one come up with the anti-derivative?
In short: Let $F$ be the anti-derivative of $f$ then $F'=f$.
Nov
28
comment Give me hints for evaluating this limit
If I am not overlooking anything this is true indeed. I guess you just need to explain your reasoning more detailed. Moreover you have to check whether you are allowed to apply my hint - if it is for a homework, then the question is whether you have already proven the hint in a lecture etc.
Nov
28
comment Give me hints for evaluating this limit
Hint. $e^x=\lim_{n\to\infty}(1+x/n)^n$
Nov
21
comment Reconstructing a function from its critical points and inflection points
@kccu Well you can just add a constant to $f$ s.t. $f(x_2)=0$ and it should be $7/7680$ if you work with rajb245's points $x_1,x_2,x_3$ - I am currently experimenting with other numbers for a better scaling but the general idea of this approach is definitely good.
Nov
21
comment Reconstructing a function from its critical points and inflection points
@whatever Well saddle points are just inflection points with the added property that $f'(x)=0$. I guess there are multiple names that are being used for both types hence the confusion. :)
Nov
21
comment Reconstructing a function from its critical points and inflection points
@whatever Every saddle point is an inflection point but not the other way round if I am not mistaken. The slope at a saddle is always zero while it does not have to be zero for inflection points.