My first intuition to derive the following function - $f(x) = \sec(x^x)$ - was to take the natural log of both sides and simplify to: $\ln(f(x)) = x(\ln(\...

$ax^3 +bx^2 + cx + d= 0$ If the roots are $\alpha$ $\beta$ and $\gamma$, Is there any relationship between the sum of the squares of the roots and the coe...

I have to evaluate $$\iint_TxdS$$ Where $T$ is the part of the sphere $x^2+y^2+z^2=a^2$ which lies in the first octant $x,y,z\geq0$. So I used polar coord...

I'm sorry I don't have the book with me (don't know the problem number) since I moved, but I still remember the problem. It said something ...

Can anyone suggest a good algorithm to create structures like this? Note that what I what I am asking for is not a true maze with one start and one soluti...

I seem to have trouble with quadratic equations when it comes to fractions and square roots. $$ \frac{1}{x}+2x=3 $$ How do I solve this equation?

If $\mathrm P(X=k)=\binom nkp^k(1-p)^{n-k}$ for a binomial distribution, then from the definition of the expected value $$\mathrm E(X) = \sum^n_{k=0}k\mat...

This question looks so simple, yet it confused me. If $f(x) = e^{\ln(1/x)}$, then $f'(x) =$ ? I got $e^{\ln(1/x)} \cdot \ln(1/x) \cdot (-1/x^2)$. And...

Q: The polygon circumscribes the circle. Find the perimeter.

This question is about set equality, as it is presented in Chapter 3, Set Theory, Section 1, Fundamentals, of Terence Tao's textbook, Analysis I. How...