I'm working through a practice test with no available solutions, and I came across this question. Let $a,b,c,d,e$ be integers with $c>0$. Suppose ...

I am studying rotation and translation of conical but have no doubt in basic concept (Sorry, I know this is a very stupid question but I'm really str...

This answer gives a really great explanation of why partial fraction decomposition works. However, the explanation implies that rational functions can be ...

I just noticed this today and I'm a bit confused by it. If we represent cos(x) as the real part of exp(ix), then I always thought that we could then ...

knowing that the characteristic of an integral domain is $0$ or a prime number, i want to prove that the characteristic of a finite field $F_n$ is a prime...

I am not too sure how to explain this in words. So the question is proofing that $a ^{\log_bc} = c ^{\log_b a}$ So far what I have done was: I cannot thin...

As the title says, I want to show that the limit of $$\lim_{x\to 0} \frac{\cos(x)}{x}$$ doesn't exist. Now for that I'd like to show in a formal...

I see a lot of calculus texts stating direct substitution is a form of evaluation for a limit. Maybe I'm missing something because, to me, direct sub...

The title says it all. In the same way that: Two distinct points determine a line. Three noncollinear points determine a plane. My question is: Do four no...

1) 2, 2 1/2, 3 1/3,... I thought the nth term here was (2^n+n-1)/n. That gave me 19/4 as the fourth term but the answer is 5. 2) 2, 2 1/2, 3 1/8,... No id...