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 Jul4 comment Proving the Product Rule for exponents with the same base How do you define this when $b$ and $c$ are not rational? Jul3 comment derivative of $f(x)=\frac{x}{x-1}$ Do you know how to use the quotient rule? What are you having trouble with specifically? Jul1 comment Evaluation of $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$ That was meant for the asker, by the way. Jul1 comment Evaluation of $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$ Also don't forget that these formulas work when $n \ge 0$, but the series in the question has $n \ge 1$. Jun30 comment Confusion regarding change of variables in ODEs It seems I just can't write comments today. I meant $g(x) = y(x+\pi)$. Jun30 comment Confusion regarding change of variables in ODEs @Shuhaho: I'm sorry, I accidentally submitted that comment early and was going to fix it but I forgot. I understand that. What I was going to say is, what's the point of using a different variable name? Like you said; isn't it clearer to say "use $g(x) = g(x+\pi)$" instead of "use $t = x - \pi$"? Jun30 comment Confusion regarding change of variables in ODEs That works. But what's the point then ofusing two different Jun23 comment Prove $\frac{\cos^2 A}{1 - \sin A} = 1 + \sin A$ by the Pythagorean theorem. Do you know the identity $\cos^2 A + \sin^2 A = 1$? Jun21 comment How to derive compositions of trigonometric and inverse trigonometric functions? @GitGud: Why shouldn't drawings count as proof? As long as you remember that the proof only works for angles smaller than $90^\circ$, they're perfectly good arguments. Jun21 comment Equivalence of Notation for Momentum Continuum That it is an abuse of notation doesn't mean it's wrong. That's why it's called abuse and not misuse. Jun17 comment Differentiability of a function at a point to prove it differentiable everywhere on the given condition. Consider the function that is $1$ at $0$ and $0$ everywhere else. Jun17 comment Why does derivation use lim? Alternative method possible! What do you mean by relativity? Jun16 comment Graphing $\sin(|x|)$? Is the sine of a positive number always positive? Jun16 comment Generelized Integral Convergence @TheAnswer: It does solve your problem, you just didn't compute the limits correctly. Both are $-\infty$, therefore the limit doesn't exist and the integral doesn't converge. Jun14 comment Solving for $x$: $1=\frac{1}{x}+\frac{1}{1+\frac{1}{x}}+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}+\cdots$ Some quick calculations lead me to believe that the series does not converge, but I might be wrong. Jun14 comment Supposedly simple integral This question may be relevant. Trying to solve the differential equation mentioned in the accepted answer leads to an integral similar to this one, so I'm not sure how useful it is. Jun13 comment Confused by $\Re(z)$ and closed contours, why isn't it the integral 0? @Sharkos: Yes, I realized that after I posted the comment. Jun13 comment Confused by $\Re(z)$ and closed contours, why isn't it the integral 0? Small tip: if you want us to tell you if there's anything wrong with your calculations, include them in the question. Jun4 comment How to calculate surface area of a curved plane? It depends on the precise shape of the surface. Is this particular one supposed to be half a cylinder? Jun3 comment Prove or disprove: if $f$ and $fg$ are continuous then $g$ is continuous. @vadim123: No, wait. If there was such a sequence, $f$ would not be continuous at $a$. You don't need $f$ to be continuous on an interval; I believe algebra of limits implies that if $f$ is continuous and non-zero at $a$, then so is $1/f$.