$$\int (\log x)^3\,dx$$ I solved the problem by applying integration by parts twice: First, I write the integrand as $(\log x)^2\cdot\log x$, and then I s...

I get how to derive the ellipse equation, but I'm struggling to understand what it means intuitively. You see, a circle equation can be understood ve...

I have seen the term "fixed matrix" being used in a lot of definitions. What does one mean when they say a "fixed" matrix? And what is this "fixed" proper...

How do you find the perimeter of a triangle given only its base and height measurements? I shall appreciate explanations which does not involve difficult ...

Poker is played with a regular deck of cards which contains 52 cards. In the deck of cards there are 4 suits (♠♡♢♣), each in 13 denominations. A hand of p...

With exponentiation, you can raise numbers to complex, irrational, etc. This is defined as such: $$\exp(x)=\sum_{n=1}^\infty{x^n\over{n!}}$$ With $e=\exp(...

I am given this problem as extra credit in my class: Propose TWO example recurrences that CANNOT be solved by the Master Theorem. Note that your examples ...

I have three variables X, Y, Z. and I know $Corr(X,Y), Corr(X,Z),Corr(Y,Z),Var(X),Var(Y),Var(Z)$. and Cov is Covariance, Corr is correlation, Var is varia...

This is from Higher Algebra by Hall and Knight, $u+v+\sqrt{uv}=39$...(1) $u^2+v^2+uv=741$...(2) we obtain by division $u+v-\sqrt{uv}=19$ I don't know...

I am trying to find the derivative of $2\sqrt{x-3}$ using the limit definition of a derivative. What I did is $$\lim_{h \to 0} \frac {2 \sqrt {(x+h)-3} -2...