Use the second order Taylor polynomials $P_2(x)$ for the given functions about the point specified to approximate the indicated value. Estimate the error ...

What do mean $\bigvee$ operator in page 6 of this document. It is a Variable-sized Math Operator. What about $\bigwedge$?

I think I have a problem with a basic understanding of partial derivatives when changing variables. I do understand that if we just change variables, e.g....

Suppose that we had a set of vertices labelled $1,2,\ldots,n$. There will several ways to connect vertices using edges. Assume that the graph is simple an...

I have to solve differential systems like this: $$ \left\{ \begin{array}{c} x' = 3x - y + z \\ y' = x + 5y - z \\ z' = x - y + 3z \end{arra...

I was wondering if there is a way to calculate the chromatic number of a graph knowing only the chromatic polynomial, but not the actual graph. Could some...

Is there, at all any relationship between the geometric mean of a set and the arithmetic mean of a set? If I knew one, and I knew the number of terms in t...

I know that if we want to convert from base 16 to base 10 we do as follows (for example): Given : $15C$ in base $16$ Conversion to base 10: $12 \times 16^...

Suppose we have a square in 3D space with its normal pointing in the direction of the positive $z$ axis, i.e. $(0,0,1)$. The four vertices of the square a...

The average rate of change for $f(x)=x^2+4x-6$ on the interval $[1,3]$ is $8$. I am not interested in final answer but more how to get there. I am going t...