The system described by $x'=2x^2-8$ is linearized about the equilibrium point -2. What is the resulting linearized equation? Answer is $x'=-8x-1...

If it's an odd degree, why isn't it always an odd function? Can you please give me an example?

Let the be the following permutation: $(1 5 4)(3 6)\in S_6$ How do I count the number of inversions to calculate the sign of the permutation? $(1 5 4)(3 6...

Apologies for the less than clear question, I wasn't quite sure how to phrase it. Say you have a random variable $X ~ N(5, 10^2)$. Say you have anoth...

Is it reasonable to use the terms Greatest Common Factor and Greatest Common Divisor interchangeably ?

How can I know if one power is bigger than the other when the bases are different? For example, considering $2^{10}$ and $10^{3}$ the former is the greate...

I've been given a problem, to calculate the convolution of the functions $h$ and $x$ where: $$h(t) = \begin{cases}t &\text{if $0<t<2T$}\\ 0...

I know with integration by parts the answer is $x\ln(x) - x$ but I was wondering how to do this without integration by parts.

Like, is their an algebraic method? For example if I am asked to find the domain of $g(t) = \sqrt{t^2 + 6t}$ , how do I determine the range of this? Is th...

I have a data set of points in three dimensions. I'm calculating the barycenter (mean) and $3\times3$ covariance matrix from this data set. I store t...