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 Aug13 comment Why can't $\int_0^1\sin(x^2) dx$ be equal to $2$? Forgive me if I'm missing something, but why would it be 2? I mean, with so many numbers to choose from, why would you expect it to be 2? Aug6 comment Projectile Motion @ladaghini: Nothing, my mistake. Aug6 comment Projectile Motion @GorillaOne: Yes, sorry, I messed that up. I'll write an answer if I figure it out. Aug6 comment Projectile Motion @GorillaOne: If you know those, you can find out the time from $x=x_0+v_x t$ Aug1 comment Derivative of $x^x$ at $x=1$ from first principles @user758556: I guess to use L'Hôpital's you would have to know $\frac{\mathrm{d}}{\mathrm{d}h} (x+h)^h$, which sorts of defeats the purpose of using the limit definition in the first place. Jul25 comment Having trouble understanding proof of a theorem involving limits of functions and sequences Oh, I get it now. I'm not sure if the argument I'm thinking of is the same one the author is describing, but whatever. Your answer sure helped, though! Jul25 comment Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals? Fun fact: In some languages, in particular Spanish, sine still has the same not safe for work meaning. This has lead to uncountable repressed giggles in high school math class. Jul22 comment Compute integral $\int_{-6}^6 \! \frac{(4e^{2x} + 2)^2}{e^{2x}} \, \mathrm{d} x$ @Matt: Isn't it simpler to just say $\mathrm{d}u = e^x\ \mathrm{d}x = u\ \mathrm{d}x \implies \frac{\mathrm{d}u}{u} = \mathrm{d}x$? Jul21 comment Compute integral $\int_{-6}^6 \! \frac{(4e^{2x} + 2)^2}{e^{2x}} \, \mathrm{d} x$ After doing the change of variables, shouldn't it be $u^2$ instead of $e^{2u}$ in the numerator? Jul21 comment Motivation for definition of logarithm in Feynman's Lectures on Physics I just saw in the feynmanlectures.info site that this has been added to the errata. Awesome! Jul20 comment Find all solutions, other than $2$ for $12x^3-23x^2-3x+2=0$ @Austin: You don't need to ask. You could just plug in those values and check whether they satisfy your equation. Jul19 comment Help solving differential equation: $y' = x\sqrt{4+y^{2}}/{y(9+x^{2})}$ The right side of the equality can be written as $\frac{\sqrt{4+y^2}}{y} \frac{x}{(9+x^2)}$. Does this help? Jul15 comment Motivation for definition of logarithm in Feynman's Lectures on Physics I get it now, thank you! This paragraph is really weird, considering that the rest of the lectures is very well written and clear. Jul15 comment Motivation for definition of logarithm in Feynman's Lectures on Physics @joriki: That really helps. Thanks! Jul15 comment Is the function $y=\ln x^2$ the same as $y=2\ln |x|$? Short answer: yes. Jul14 comment Problems regarding exponents @Rick: Yeah, I think I'll change it. Thanks for the advice! Jul7 comment I have to show $(1+\frac1n)^n$ is monotonically increasing sequence Unless I'm missing something, that sequence is increasing, not decreasing. Jun30 comment Does this weird sequence have a limit? That's interesting. Does this change if instead of picking a number from ${1,2,3,4,5,6}$ we choose a random real number, or maybe one from the interval $[0,1]$? Jun30 comment Does this weird sequence have a limit? @anon: Making a needlessly complicated definition was sort of the point. Also, you don't necessarily have to choose $k$ randomly. You can start from $1$ and work your way up if you want; the point is not so much in what order the terms are calculated, but that you can calculate $a_k$ for any $k$ you want. Jun30 comment Does this weird sequence have a limit? @AndréNicolas: What I mean if that $a_k$ has already been calculated, there is no need to roll the die again. We just look at the list and check what was the value of $a_k$.