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location Canada
age 32
visits member for 1 year, 7 months
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I hold a diploma in Network Administration (along with many industry certifications) and am currently studying Computer Science and Pure Math in University.


Mar
11
asked How can i show that any two arbitrary intervals in the set of reals have the same cardinality?
Mar
11
asked Let $A$ and $B$ be arbitrary sets. Show that $|A\times B|=|B\times A|$
Mar
11
accepted Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
Mar
11
comment Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
@Lubin Well, I passed it in using the trig identity... It only said "Hint: Use integration by parts". So I didn't bother, since it was easier otherwise. If I lose marks then I lose marks.
Mar
11
comment Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
Why is $\sin{kx}$ and "odd" function?
Mar
11
revised Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
added 325 characters in body
Mar
11
comment Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
I'm not quite sure I understand how you got where you did - is that a typo? Shouldn't it be $\cos{(x(m-n))}$? Also, when I follow that procedure, like what wolfram alpha does, I get to a scenario where if $m=n$, then when I plug into the formula, I end up dividing by 0.
Mar
11
comment Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
I don't suppose I have to... but the hint on the assignment says to do so.
Mar
11
asked Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts
Mar
10
comment How do I solve $\int\frac{\cos^2(x)}{\sin(x)}\ dx$ without using Weierstass Substitution?
Indeed I should have known that... I'm starting to think that my brain is going numb from all the trig integrals I've done. Thanks for the insight.
Mar
10
asked How do I solve $\int\frac{\cos^2(x)}{\sin(x)}\ dx$ without using Weierstass Substitution?
Mar
10
comment How to integrate $\int\frac{1}{1+\cos{x}}\ dx$?
I'll definitely have to look into this method. I don't recall being taught it, but it looks like it might be very helpful in the future.
Mar
10
accepted How to integrate $\int\frac{1}{1+\cos{x}}\ dx$?
Mar
10
asked How to integrate $\int\frac{1}{1+\cos{x}}\ dx$?
Mar
10
accepted What does the notation $2\mathbb{Z}$ mean?
Mar
10
comment How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite?
I like that - didn't think to divide the exponent by two.
Mar
10
comment How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite?
Ohh.. ok, I think I see now - But I think for the purposes of this assignment, it'd be more work to do it this way because I'd have to show not only this, but I'd have to demonstrate that $\mathbb{Z}$ is countably infinite first.
Mar
10
comment How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite?
But this doesn't show a bijection from $\mathbb{N}$... I'm confused.
Mar
10
asked How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite?
Mar
10
comment What does the notation $2\mathbb{Z}$ mean?
I think a slightly better notation would be $f:2\mathbb{Z}\to 17\mathbb{Z}:2x\mapsto 17x,\forall x\in\mathbb{Z}$