leo
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 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 22 revised Why if a function is holomorphic and injective in neighbourhood of $x_0$ then $f'(x)\ne 0$ in neighbourhood of $x_0$? deleted 2 characters in body; edited title Jul 21 revised Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$? edited tags 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 19 revised Find $\frac{d^2y}{dx^2}$ as a function of $x$ if $\sin y+\cos y=x$ added 12 characters in body; edited title Jul 17 awarded Great Question Jul 14 revised Prove $A = (A \setminus B) \cup (A \cap B)$ edited tags Jul 13 answered if $\epsilon >0$, then there exists $\delta > 0$ such that if $Q$ is partition with $||Q||< \delta$, then $L(Q;f) \geq L(f) - \epsilon$ Jul 13 revised Possible values of $\int \frac{dz}{\sqrt{1-z^2}}$ over a closed curve in a region? Typo. Jul 3 awarded Revival Jul 3 answered Why is every conformal bijection between disks a linear fractional transformation? 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. Jul 1 revised Integration of powers of the $\sin x$ English 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. Jun 2 revised Winding number of a point outside the curve is 0 Fixing title. TeXing May 18 revised Does the set of differences of a Lebesgue measurable set contains elements of at most a certain length? added 3 characters in body