I am having trouble with this question: if f(x) is a continous function and $$ 1 - x^2 \leq f(x) \leq e^x $$ for all values of x, calculate $$ \lim_{x\to0...

I'm trying to prove that $$\mathcal{L}\{t^2e^{at}\} = \frac{2}{(s-a)^3}.$$ I've gotten to the last integration by parts where $$ \lim_{n\to\inft...

When do two functions become equal? I have stumbled over this definition of equality of functions in elementary real analysis. Let $X$ and $Y$ be two sets...

It seems that the solitaire card game 'klondike' presents some head scatching when trying to work out odds for winnable games etc, but I would i...

How many possible combinations can a 3-digit safe code have? Because there are 10 digits and we have to choice 3 digits from this, then we may get $10^P3$...

Find the interval $[a,b]$ for which the value of the integral $\int_{a}^{b} (2+x-x^2)dx$ is maximized. To solve this problem, I believe I need to the larg...

I'm currently trying to learn abstract algebra myself, and the following is a quote from the book I am using, "A set of equations, involving only the...

The numbers of the roots of $e^x + 0.5x^2 -2 = 0$ in the range $[-5, 5]$ are ________ . My try: Someone explained using intermediate value theorem, and so...

I need some how with the power reducing formula. I'm having trouble understanding how to apply it. Here's an equation that utilizes it: $\cos^2 ...

sorry for the dumbest question ever, but i want to understand total order in an intuitive way, this is the defition of total order: i) If $a ≤ b$ and $b ≤...