Trying to understand what the differnce is between a vertical and horizontal line test. If an equation fails the vertical line test, what does that tell y...

What is the definition of the negation of a statement? I know that if a statement is true then its negation is not true and also that either the statement...

Apologies, this is a simple question but I seem to have some sort of brain freeze. I'm looking for the range of this piecewise function: $$f(x)=\begi...

I am currently learning about the Trig addition formula. The book I am reading has a proof for it. The proof is attached here: However, I have a question ...

Find the relative maximum and relative minimum of the function $f(x) = 49x + \frac{4}{x}=49x+4x^{-1}$ Solution: Step 1: Find the values of $x$ where $f�...

I'm having trouble figuring out how to compute the iterated logarithm (log-star) by hand without using a calculator or programming language. I wrote ...

Suppose we have a function $\phi$ so that $$\phi (x)=\cases{f(x) & \text{ if } x\le 0\\ g(x)& \text{ if } x>0.}$$ where $f$ is continuous on $(...

Take a complex number $z=u+iv$ and call its magnitude $x$. Consider the real and imaginary parts to be Gaussian distributed: $$ f_{U}(u)=\frac{1}{\sqrt{2\...

In naieve set theory, you quickly run into existence trouble if you try to do meta-things things like take "the set of all sets". For example, does the se...

Consider a divergent $p$-series with $p<1$, for instance $\sum_{j=0}^{\infty} \frac{1}{\sqrt{j}}$. Let $R_{n}=\sum_{j=n}^{\infty} \frac{1}{\sqrt{j}}$ b...