updates
How is this step acheived? $h(x)= 27x^6+26x^3-1 $
Find all real roots of $h(x)$. Solution I have solved the question by letting $u = x^3$ and then using the quadratic formula to solve $27u^2+26u-1 = 0$. H...
Apr 19, 2026
Archive: Updates
updates
Solving second-order ODE using an integrating factor
Solve the ODE $$ \frac{\partial^{2} u }{\partial \eta^{2}} + \frac{\eta}{2\nu} \frac{\partial}{\partial\eta} = 0 $$ The book uses integrating factor = $ e...
Apr 19, 2026
updates
Finding vertices of regular polygon
I am trying to find the vertices of a regular polygon using just the number of sides and 2 vertices. After the second vertex, I will make left turns to fi...
Apr 19, 2026
updates
How to integrate $e^{\sin x}(x \cos x - \tan x \sec x)$
How would on find the indefinite integral $e^{\sin x}(x \cos x - \tan x \sec x)$ Our professor gave it to us as a review question. He told us it was from ...
Apr 19, 2026
updates
When working with unit vectors, do we consider the scallor part?
I want to know for perhaps computing dot products etc, that if Im just told the angle between to unit vectors...say pi/6, how would I find the dot product...
Apr 19, 2026
updates
Where to choose the point of expansion for taylor series?
Typically, in taylor series, I see an expansion about $x=0$ for some function $f(x)$ that we're approximating. I always thought this was just done fo...
Apr 19, 2026
![Prove that $\operatorname{trace}(ABC) = \operatorname{trace}(BCA) = \operatorname{trace}(CAB)$ [closed]](https://news.conceivablytech.com/uploads/prove-that-operatorname-trace-abc-operatorname-trace-bca-operatorname-trace-cab-closed_720.jpg)
updates
Prove that $\operatorname{trace}(ABC) = \operatorname{trace}(BCA) = \operatorname{trace}(CAB)$ [closed]
Prove that $\operatorname{trace}(ABC) = \operatorname{trace}(BCA) = \operatorname{trace}(CAB)$ if $A,B,C$ matrices have the same size.
Apr 19, 2026
updates
Inverse Fourier transform of $ \frac1{a+\mathrm{j}w} $
The Fourier transform of $f(t)$ is defined as $$F(\mathrm{j}w)=\int_{-\infty}^{\infty}f(t)\,\mathrm{e}^{-\mathrm{j}wt}\,\mathrm{d}t,$$ while the correspon...
Apr 19, 2026
updates
Approximating log of factorial
I'm wondering if people had a recommendation for approximating $\log(n!)$. I've been using Stirlings formula, $ (n + \frac{1}{2})\log(n) - n + \...
Apr 19, 2026
updates
Diagonalizing a 3x3 matrix
Prove that matrix $A$ is diagonalizable, find the bases for the eigenspaces, the diagonalizing matrix $P$, and compute $P^{-1} A P$ where $A= \left(\begin...
Apr 19, 2026
