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Note: Conversion is based on the latest values and formulas.
inequality - Prove $|x|^2$ = $x^2$ - Mathematics Stack Exchange Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
How is $x^2$ related to $x^Tx$ - Mathematics Stack Exchange Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
integration - how to calculate the integral of $\sin^2(x)/x^2 ... 6 May 2012 · Hence the answer separates $\frac{\sin^2{x}}{x^2}$ into three parts all which have singularity at zero. The upper and lower are picked in a way that controls the growth of the …
Proof of $\\sin^2 x+\\cos^2 x=1$ using Euler's Formula Multiply $\mathrm e^{\mathrm ix}=\cos(x)+\mathrm i\sin(x)$ by the conjugate identity $\overline{\mathrm e^{\mathrm ix}}=\cos(x)-\mathrm i\sin(x)$ and use that ...
What's the difference between $(-x)^2, -x^2$ and $-(x)^2$? In the expression $(-x)^2 = (-x)\cdot(-x) = x^2$ they are essential. This convention is very similar to the way that $$3-2\cdot 4 = 3 - (2\cdot 4)$$ must be handled. $^\ast$ some programming …
calculus - Derivative of ${x^{x^2}}$ - Mathematics Stack Exchange Studying past exam problems for my exam in ~$4$ weeks, and I came across this derivative as one of the questions. I actually have no idea how to solve it. $$\\frac{d}{dx} (x^{x^2})$$ Using the chain
statistics - What is the expectation of $ X^2$ where $ X$ is ... Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
real analysis - How can I prove that $xy\leq x^2+y^2 Technique 1:$$\sqrt{x^2y^2} = xy \le \dfrac{x^2 + y^2}{2}\le x^2 + y^2$$ Technique 2:$$(x - y)^2 \ge 0 \implies x^2 +y^2 - 2xy \ge 0 \implies x^2 + y^2 \ge 2xy\ge xy$$ Technique 3 (my favorite): …
What is the integral of $e^{-x^2/2}$ over $\\mathbb{R}$ What is the integral of $$\int_{-\infty}^{\infty}e^{-x^2/2}dx\,?$$ My working is here: = $-e^(-1/2x^2)/x$ from negative infinity to infinity.
Solving $2^{16^x} = 16^{2^x}$ - Mathematics Stack Exchange 13 Nov 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, …