Prove that every Cauchy sequence in $\mathbb{R}$ converges. proof: Let $A_n$ be a closed and bounded sequence. Then there exists an interval $[a_1,b_1]$ s...

My Problem: x mod(3) = 2 x mod(5) = 4 x mod(7) = 1 Solve for x I was given a formula x = (x mod(3) * 70 + x mod(5) * 21 + x mod(7) * 15) mod(105) to solve...

The following are exercises from The Four Pillars of Geometry; I'm not sure what they are stating, for example I don't know what the addition of...

The first derivative can tell me about the intervals of increase/decrease for $f(x)$. The second derivative can tell me about the concavity of $f(x)$. So ...

Hello I' am stuck on how to get the final result of the laplace transform of $f(t)=tsin(at)$using (a is a constant) only the definition of $$\int_0^{...

I've been reading into Fubini's theorem (rectangular regions) quite extensively over the last few days, and I've gathered the following: Fo...

On Wikipedia, a parabola is defined as follows: A parabola is a set of points such that, for any point $P$ of the parabola, the distance $|\overline{PF}|$...

I am reading a book that explains elementary number theory: Number Theory: A Lively Introduction with Proofs, Applications, and Stories by James Pommershe...

I'm confused by what my solution manual is telling me. Part a of a problem I'm doing is: Sketch the plane curve with the given vector equation. ...

. How to write these ratios $X:Y:Z$ in terms of fraction i.e. either like $$\frac{\frac{X}{Y}}{Z}$$ or $$\frac{X}{\frac{Y}{Z}}$$?