How do I prove that $x^2 + y^2 = (x + y) ^2 – 2xy$ geometrically ...
May 9, 2015 · $\begingroup$ Zannah, you're allowed to start on the right side: Compute $(x + y)^2 = (x +y)(x+y)$, the usual mnemonic being "FOIL". Then subtract $2xy$ from his. Then subtract …
calculus - Implicit derivative of $x^2+y^2=(2x^2+2y^2-x)^2 ...
Sep 2, 2020 · The denominator is also equal to zero for $$ y \ = \ 0 \ \ \Rightarrow \ \ x^2 \ = \ (2x^2 - x)^2 \ \ \Rightarrow \ \ 4x^4 \ - \ 4x^3 \ \ = \ \ 0 \ \ \Rightarrow \ \ 0 \ , \ 1 \ \ . $$ So there …
calculus - How to integrate $\int \sqrt {x^2+a^2}dx
May 15, 2013 · I will give you a proof of how they can get the formula above. As a heads up, it is quite difficult and long, so most people use the formula usually written in the back of the text, …
How do I prove $2xy ≤ x^2+y^2$? - Mathematics Stack Exchange
Oct 7, 2018 · How do we prove without calculus that $\forall \ x,y \ge 0$, we have $\ 1+x^3+y^3\ge x+x^2y+y^2$ Hot Network Questions Problem with more than one macros in tikz's foreach loop
calculus - Power series representation of $(x+a)/(x^2+a^2 ...
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Proof $f(x,y)=xy(x^2-y^2)/(x^2+y^2)$ continuous everywhere.
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calculus - How do I solve $yy'+x=\sqrt{x^2+y^2}$? - Mathematics …
The $x^2+y^2$ suggests using polar coordinates. Substitute $x=r\cos\theta$ and $y=r\sin\theta$. The difficult bit is the expression for $dy/dx$.
probability - Why is the expected value $E(X^2) \neq E(X)^2 ...
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calculus - Valid proof for integral of $1/(x^2+a^2)$ - Mathematics ...
Mar 3, 2023 · The usual attack for this integral is to "pull a rabbit out of a hat": most books will say something like. Hey, remember back in Chapter 4 where we used the inverse function theorem …
Find all real solutions for $x$ in $2(2^x- 1) x^2 + (2^{x^2}-2)x = 2 ...
Feb 12, 2015 · Any exponential with 2 as it's base get's it's exponent reduced by 1 when divided by 2. then we have: $(x^2-1)x^2 + (2^{x^2-1} - 1)x = 2^x-1$, the difference from what you got …