The problem Can be $\zeta(3)$ written as $\alpha\pi^\beta$, where ($\alpha,\beta \in \mathbb{C}$), $\beta \ne 0$ and $\alpha$ doesn't depend of $\pi$...

Let $$f(x)= \begin{cases} 5 &\text{, x $\geq$ 0}\\ x^2 &\text{, x < 0} \end{cases}$$ and $$g(x)= \begin{cases} \sqrt{x} &\text{, x > 3}\...

In calculus, the antiderivative (indefinite integral) can be considered as the reverse operation of a derivative. A gradient yields a vector. Is there a s...

How do I prove that $x=\text{sup}\{q\in \mathbb{Q}:q<x\}$? Provided that $x\in\mathbb{R}$...

I was told to assume that $$\ln b=\lim_{h\to 0} \frac{\left(b^h-1\right)}{h}$$ where b is a positive, real, base. Unfortunately, being told to assume some...

I'm now reading about the formal definition of line as the graph of the function $f(x)=f(x_0)+m(x-x_0)$ for an arbitrary $x_0$ through which the grap...

Let us define a very simple integral: $f(x) = \int_{a}^{b}{x}$ for $a,b\ge 0$. Why do we have the identity $\int_{a}^{b}{x} = -\int_{b}^{a}{x}$? I drew th...

Use Fermat's Little Theorem to find the remainder of $5^{15}$ divided by $1337$. I know Fermat's Little Theorem, but failed to understand how to...

What is the value of $$\lim_{x\to\infty}\frac{\sqrt{x^4-1}}{2x^2+3x-1}$$ I tried to factorise the denominator or the numerator but it takes me nowhere. My...

Here is the all identities : http://en.wikipedia.org/wiki/Vector_calculus_identities I need help concerning vector functions and indexing notations. Let $...