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 Mar 14 revised How to compute this integral using residues. edited tags Mar 14 revised How to compute this integral using residues. added 6 characters in body Mar 14 comment Martingale property for two stochastic processes $B_t-B_s|\mathcal{F}_s$ has normal distribution with mean $0$ and variance $t-s$ Mar 13 comment Constructing a partition and sigma algebras what is $\sigma(E)$? Mar 13 revised Integral inequality for a Cauchy exponential series product added 8 characters in body Mar 13 revised Why $\frac{1}{2}\ln |2x+7| + K = \ln|2x+7|^{1/2}+\ln k$ added 1 character in body; edited title Mar 11 revised A sequential problem edited tags Mar 11 revised Integrate $\int \frac{ e^{\tan^{-1}x}}{(1+x^2)^2} dx$ added 1 character in body Mar 11 revised Integrate $\int \frac{ e^{\tan^{-1}x}}{(1+x^2)^2} dx$ added 1 character in body Mar 11 revised Integrate $\int \frac{ e^{\tan^{-1}x}}{(1+x^2)^2} dx$ edited title Mar 11 comment Integrate $\int \frac{ e^{\tan^{-1}x}}{(1+x^2)^2} dx$ you want to use a substitution $u = \tan^{-1} x$ so $du = \frac{dx}{1+x^2}$, not sure how to get rid of the second $(1+x^2)$ in the denominator Mar 11 answered How do I prove these matrices have the same rank? Mar 11 revised Heat flow equation via Fourier Series deleted 2 characters in body Mar 11 comment Projectile Motion Question @MB You can explicitly compute the maximum height since the projectile itself (in each direction) follows a parabola $S_t = S_0 + v_0 t - gt^2/2$, so the maximum occurs at $t = v_0/g$.... Mar 11 revised Projectile Motion Question added 20 characters in body Mar 11 answered Projectile Motion Question Mar 11 revised Projectile Motion Question edited tags Mar 11 answered If $(\xi_k), k \ge 0$ is a sequence of iid Gaussian variables, does it hold a.s. that $\sum \xi_k^2 = +\infty$? Mar 9 revised Does $a_n$ increasing imply $a_n-\frac{1}{n}$ strictly increasing? deleted 1 character in body; edited tags Mar 9 comment Prove that $\displaystyle \lim_{x \to a} f(x) = \infty$ iff $\displaystyle \lim_{x \to a} \frac{1}{f(x)} = 0$ @Puzzled417 it is talking about the same $f$ in the second part...