I (sort of) understand what Taylor series do, they approximate a function that is infinitely differentiable. Well, first of all, what does infinitely diff...

I have to put some data together for a presentation on lakes that will be affected by a rule change. I have a table with the surface area of the lake and ...

If you were to flip a coin 150 times, what is the probability that it would land tails 7 times in a row? How about 6 times in a row? Is there some forumul...

By Cayley's theorem, we know that for any finite group $G$, there exists $N \in \mathbb{N}$ such that $G$ is isomorphic to a subgroup of $S_N$, the s...

I'm trying to prove that $a\cdot b=b\cdot a$ when $a$ and $b$ are two natural numbers. In the rest of this question I'm using $a'$ for the s...

$$f(t)=\frac{\sin^3(\pi t)}{(\pi t)^3}$$ I want to calculate the Fourier transform. I can't calculate this integral: $$\int_0^\infty\frac{\sin^3(\pi ...

We have 3 boxes. In every one there are 2 balls. One of them has 2 black balls, second 2 white balls, third black and white ball. On every box is a right ...

I'm trying to learn Complexity classes.I want to show Hamiltonian cycle is NP Complete. The text tells me that Inorder to prove NP-Completeness we fi...

Can you help me with solving this integral $$\int \cosh^4(7x) \, dx \text{ ?}$$ I tried use subs but i got $$\cosh^4(t)=m$$ $$t = \pm\operatorname{arccosh...

I have the following series : $$\sum_{k=1}^{\infty }\left ( \frac{k}{\sqrt{4k^{3}+1}} \right )$$ And I am trying to see if it's convergent or diverge...