I've been told that pi is an irrational (infinite and non-repeating) number. But to what extent is it non-repeating? It obviously repeats individual ...

An imaginary point is defined as an ordered pair of values, at least one of which is complex. My text says that if $h^2 < ab$ in the equation : $$ ax^2...

I know smilar questions have been asked and I have looked at them but none of them seems to have satisfactory answer. I am reading the book a course in ma...

If in a group $G$, $a^5=e$, $aba^{-1}=b^2$ for some $a,b\in{G}$. Find $o(b)$. I wrote $aba^{-1}=b^2$ as $ab=b^2a$. Then $(ab)^5=(b^2a)^5$ but then I am st...

How do you show $$\lim\limits_{k \rightarrow \infty} \frac{\left(2+\frac{1}{k}\right)^k}{2^k}=\sqrt{e}$$ I know that $$\lim\limits_{k \to \infty} \left(1+...

I know that this is sometimes the case, but that some matrices are not tensors. So what is the intuitive and specific demands of a matrix to also be a ten...

I have this string of questions, but when I look up depressed cubic, I don't quite understand. I'm not asking for all of these questions to be a...

I'd like to know how to integrate $$\frac{4x}{x^3+x^2+x+1}$$ Please could anyone help me Thanks all

Integrate $\int x\sin^2 (x) dx$ My attempt: $$=\int x\sin^2 (x) dx\\ =x^2\sin^2 (x) - \int 2\sin (x)\cos (x)x^2 dx\\ =x^2\sin^2 (x) - \int \sin (2x) x^2 d...

The number $137$ is a prime number.One of the permutation of $137$ is $173$, which is a prime number. The summation of $137$ digits is $11$ which is again...