$A \in B$ vs. $A \subset B$ for proofs
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$A \in B$ vs. $A \subset B$ for proofs

I have to prove a few different statements. The first is if $A \subset B$ and $B \subset C$ then prove $A \subset C$. This one is fairly straight forward,...

Published: Aug 15, 2026

$\int_0^{+\infty}{ \sin{(ax)} \sin{(bx)}}dx=?$
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$\int_0^{+\infty}{ \sin{(ax)} \sin{(bx)}}dx=?$

How can I calculate the integral: $$\int_0^{+\infty}{ \sin{(ax)} \sin{(bx)}}dx$$ ?? I got stuck.. :/ Could you give me some hint?? Do I have to use the fo...

Published: Aug 15, 2026

Proof of Descartes' theorem
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Proof of Descartes' theorem

I came across the use of Descartes' theorem while solving a question.I searched it but I could only find the theorem but not any proof.Even Wikipedia...

Published: Aug 15, 2026

Anyone familiar with a mathematical symbol for
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Anyone familiar with a mathematical symbol for "that is" / "to clarify" / "whereby"?

Many years ago, a math teacher of mine thought us that there was a mathematical symbol for "that is" / "to clarify" / "whereby" (I'm not from an Engl...

Published: Aug 15, 2026

Using Lagrange Multipliers to determine the point on a surface nearest to P
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Using Lagrange Multipliers to determine the point on a surface nearest to P

I'm attempting to figure this problem out. I would appreciate some guidance on how to get the answer. Thanks. Consider the surface defined as $S: x^2...

Published: Aug 15, 2026

$ (e^{2x})=(e^x)^2$ Can Some one explain how these two are the same? I know it is trick, but I cannot see how it fits into the exponent rules.
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$ (e^{2x})=(e^x)^2$ Can Some one explain how these two are the same? I know it is trick, but I cannot see how it fits into the exponent rules.

$ (e^{2x})=(e^x)^2$ Can Some one explain how these two are the same? I know it is trick, but I cannot see how it fits into the exponent rules.

Published: Aug 15, 2026

Derivative of exponent
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Derivative of exponent

Looking to solve : $$ \frac{d}{dx}[2^{0.5x}]$$ The multiplication and X value in the exponent is confusing me. Help? Thanks!

Published: Aug 15, 2026

Solving $\sin 3\theta=1/2$ on the interval $[0,2\pi]$. I don't understand where some solutions came from.
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Solving $\sin 3\theta=1/2$ on the interval $[0,2\pi]$. I don't understand where some solutions came from.

I am learning precalculus, and I understand how to obtain first two solutions, but I don't understand where did last four solutions came from: All va...

Published: Aug 15, 2026

Problem using Casio fx-991CE X calculator to solve
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Problem using Casio fx-991CE X calculator to solve "e^(i*pi)" [closed]

I'm trying to solve e^(i*pi) on a Casio fx-991CE X calculator. The calculator is in Complex mode (MENU>2:Complex). I Input e^(i*pi) and press &quo...

Published: Aug 15, 2026

finding a basis for $W^\perp$ and understanding it.
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finding a basis for $W^\perp$ and understanding it.

Given $$ w_1 = \begin{bmatrix} 1 \\ -1 \\ 1 \\ 1 \end{bmatrix},w_2= \begin{bmatrix} 0 \\ 1\\2\\3 \end{bmatrix} $$ let $W$ be the subspace spanned by the g...

Published: Aug 15, 2026

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