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2d
comment How to find triple integral of the following question?
For some basic information about writing math at this site see e.g. here, here, here and here.
2d
comment Can we prove that matrix multiplication by its inverse is commutative?
Isn't this asking the same as this?
Jul
30
comment Is proving $m(E) < \epsilon, \forall \epsilon > 0$ equivalent to prove $m(E) = 0$?
@DavidC.Ullrich That looks like an answer.
Jul
30
comment Set-theoretic equality
The overlining is for the complementary set?
Jul
28
comment Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.
@tacos_tacos_tacos here is the same integral calculated using a rectangular contour.
Jul
26
comment Is there a proof for the maximum principle without the Cauchy integral theorem?
@DanielFischer That's an answer :-)
Jul
26
comment A question about complex integration of $\frac{1}{p(z)}$
This is perfectly fine. And the reason why both integrals are equal is either by residues theorem or noting that those circles are homotopic.
Jul
26
comment Geometric mean never exceeds arithmetic mean
Which is in here
Jul
26
comment $|g(x)| \leq K \int_a^x|g| \ \ \forall x \in I$
See this answer.
Jul
25
comment Prove that a subset of a separable set is itself separable
That's not the case, $d(x_i,e_{(i,j)})\lt r_j$. And that's because each $e_{(i,j)}$ is choose to be a point of $B(x_i,r_j)$.
Jul
25
comment Prove that a subset of a separable set is itself separable
@Wanderer Done.
Jul
23
comment Some way to integrate $\sin(x^2)$?
Oh well it's concavity.
Jul
23
comment Some way to integrate $\sin(x^2)$?
How does one get the estimate $\cos\left(\frac\pi2 t\right)\geq 1-t$? Drawing the things it's obvious.
Jul
23
comment Integrating Fresnel Integrals with Cauchy Theorem?
possible duplicate of Some way to integrate $\sin(x^2)$?
Jul
20
comment Problem about $\lim \limits_{x \to c} f'(x) = l $ implies $f'(c) = l$
Hello, given that you solved completely your problem I encourage you to add your own answer, to keep what you've learned somewhere, make it useful for others and keep this out from the unanswered queue :-)
Jul
1
comment Prove that if $a,b \in \mathbb{R}$ and $|a-b|\lt 5$, then $|b|\lt|a|+5.$
This answer does contain enough detail.
Jun
29
comment Roots of Legendre Polynomial
Roots are simple
Jun
23
comment $z_0$ non-removable singularity of $f\Rightarrow z_0$ essential singularity of $\exp(f)$
Regarding your explanation that if $z_0$ is a pole of then it's an essential singularity of $e^f$, you claim that the image of some open disk contains the complement of a disk. The definition of being a pole implies that the image of some disk is contained in the complement of a disk, I fail to see the inclusion in the other direction. How do you find a disk, such that any $z$ outside has a preimage?
Jun
2
comment Winding number of a point outside the curve is 0
Cauchy's Theorem for an open disk is enough here.
May
12
comment Sum of distances for vertices lying on a circle
Ahlfors's Complex Analysis, Exercise 3, page 80.