How can I prove Morera's theorem? Morera's Theorem: If a function $f(z)$ is continuous in a simply connected region and its integration over a c...

Find the absolute extrema of the function $f(x)=x^2-2x-2$ on $[0,1]$ To find a the extrema of a continuous function $f$ on a closed interval $[a,b]$, use ...

My textbook states the theorem that if a sequence of random variables converges almost surely, it also converges in probability, but that the opposite doe...

I was wondering if anyone could help with the below. I don't usually write maths so I'm not even sure what I'm trying to search for. I want...

Refer to the graph below: The points $(3,0)$, $(x,0)$, $(x, \frac{1}{x^2}),$ and $(3, \frac{1}{x^2})$ are the vertices of a rectangle where x $\ge$ 3, as ...

I am so confused in the usage of the words: Map and Mapping. For example, consider the mapping: $T:W^{2,p}(\Omega)\rightarrow L^{p}(\Omega)$ defined by $T...

$6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(x - 1) + c$ Find the value of A, B and C. I started it like this: $6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(...

Suppose $\mathcal{A}$ and $\mathcal{B}$ are categories with products, and $T$ a functor between them. If $X$ and $Y$ are objects in $\mathcal{A}$, what do...

I am looking at my double integration example problems and I see a note that says integral of $e^{-x^2}$ is not an elementary function. What does that mea...

Given the following expressions: 0.3² = 0.09 0.025² = 0.000625 I can head count 3*3 and 25*25, which helps me solve the above expressions. But how do I kn...