in_wolframAlpha_we_trust
Reputation
1,972
Next privilege 2,000 Rep.
 Mar16 awarded Yearling Dec9 awarded Caucus Nov4 comment Monotonicity of the function in some near interval of a local maximum critical point @iMath If that is your definition then a constant function, e.g. $f(x) = 5$ has a local maximum at every point (since there are no nearby values greater than $5$) but it's not increasing or decreasing (depending on your definition of increasing and decreasing). Nov3 answered Monotonicity of the function in some near interval of a local maximum critical point Sep30 awarded Explainer Sep26 revised differentiating a function of a function $w=\sqrt{u^2+v^2}$ This is not a question about differential equations - retagged. Sep26 suggested approved edit on differentiating a function of a function $w=\sqrt{u^2+v^2}$ Sep5 awarded Nice Answer Aug4 comment Why is $f(x)=\sin (2x-\pi)$ the same as $g(x)=-\sin(2x)$? @user50224 Look at my comment on your original posting. Aug4 comment Why is $f(x)=\sin (2x-\pi)$ the same as $g(x)=-\sin(2x)$? Step E: If you move $\sin(2x)$ by $\pi$ you get $\sin(2(x - \pi)) = \sin(2x - 2\pi) = \sin(2x)$. What you have actually done is moved it right by $\pi/2$ which is only half a period, hence the negative. Jun13 comment how do we interpret this integral from polar co-ordinates @DavidH For what it's worth, I'm pretty sure he wants your interpretation of the integral. Jun13 comment how do we interpret this integral from polar co-ordinates @DavidH Indeed. I did ask in the comments what he intended but he was adamant they were the same $r$. Jun13 answered how do we interpret this integral from polar co-ordinates Jun13 comment how do we interpret this integral from polar co-ordinates Should this really be $dr$?(and not $ds$?) May12 comment Numerical one-step method: initial value and non consistent method I think your explanation is good. Apr29 comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$? @1950RobertLewis I understand he's not a great guy, but he makes great tools. My username should really be "in_wolfram_alpha_we_trust" Apr29 comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$? @1950RobertLewis Who would you have me follow? :P Apr29 comment How can I show that ~ is an equivalence relation such that $x$~$y$ if there is a continuous path in $M$ from $x$ to $y$? What is the definition of an equivalence relation? What properties should it satisfy? How can we show that this relation satisfies these properties? Apr25 revised Explanation and Proof of the fourth order Runge-Kutta method Minor edits. Apr8 comment Second order Diff. Equation Yeah, I filled in the details. It looks like that integral doesn't have a solution in terms of elementary functions. This is (I think) the best we can do.