Write a Matlab function that applies the Gauss three point rule to N sub-intervals of $[a, b].$ The input parameters should be the name of the function be...

I am having problems understanding how to find the maximum value from a rate of change (derivative) function. The rate of change of Volume with respect to...

Let $$\lim_{x \to a} f(x) = L$$ $$\lim_{x \to a} g(x) = M$$ Where $L$ and $M$ are finite reals. Then I want to prove that $$\lim_{x \to a} f(x) g(x) = LM$...

Let $f(x, y) = x \cos(πy) − y \sin(πx)$ Find the second-order Taylor approximation for $f$ at the point $(1, 2)$. I believe the formula for 2nd order Tayl...

I would like to know if there is a mathematical approach to finding the LCM of $(29^{17} +2 , 29^{17} -1)$? Even if we would rearrange it to a fraction of...

I'm not sure how the matrix multiplication at the second image works is it a typo or is my understanding of matrix multiplication flawed. Full soluti...

Given a Cartesian vector $x \in \mathbb{R}^3$, and suppose we wish to find the coordinates $(x'_1, x'_2, x'_3)$ of $x$ in a new rotated coo...

I have only a basic understanding of mathematics, and I was wondering and could not find a satisfying answer to the following: Integer numbers are just sp...

Nakayama's lemma states that given a finitely generated $A$-module $M$, and $J(A)$ the Jacobson radical of $A$, with $I\subseteq J(A)$ some ideal, th...

Prove if $A$, $B$, and $C$ are square matrices and $ABC = I$, then $B$ is invertible and $B^{-1}= CA$. I know that this proof can be done by taking the de...