general
Limit of $\cos(x)/x$ as $x$ approaches $0$
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...
Apr 11, 2026
Archive: General
general
Simplify $\ln(|x-x^2|) - \ln(|x-1|)$
As the topic says, I need to simplify: $$\ln |x-x^2| - \ln |x-1| $$ I don't know how to approach the problem at all. I'm not asking for the answ...
Apr 11, 2026
general
Determine the amplitude, period, and phase shift of $f(t) = 2 sin t + \sqrt{3}cos t$
For the given : $f(t) = 2sint + \sqrt{3}cost$, we are tasked to find the amplitude, period and phase shift. From the book : $f(t) = 2sint + \sqrt{3}cost$ ...
Apr 11, 2026
general
Equations for different quadrants of a circle
In the circle $x^2$ + $y^2$ = $a^2$, what's the general equation for the arcs in each of the quadrants?
Apr 11, 2026
general
Rationalizing a Denominator with Cube Roots
Rationalize $\dfrac{1}{\sqrt[3]{p^2}+\sqrt[3]{pq}+\sqrt[3]{q^2}}.$ How would I go about doing this without wading through lots of algebra? Is there a tric...
Apr 11, 2026
general
Showing that a system of equation is inconsistent
When working out this system of equations, I've found that there are no solutions. Is there any way from the start you can Identify that this system ...
Apr 11, 2026
general
Linear transformation of a sphere
In $\mathbb{R}^n$, given a linear transformation $A$ represented by a matrix $(A_{ij})$, it makes sense that $A: \mathbb{R}^n \to \mathbb{R}^n$ maps the u...
Apr 11, 2026
general
Proof that the set $\{ x \in R^n | Ax \leq b, Cx = d \}$ is convex
I need a help with prooving that a given set is a convex set: $\{ x \in R^n | Ax \leq b, Cx = d \}$ I know the definition of convexity: $X \in R^n$ is a c...
Apr 11, 2026
general
how does $2*4*6....(2n)$ turn into $2^n* n! $ in this power series?
How do they change the denominator from the equation into $2^{n}n!$ in this case? Isn't it just $2n$ as $n$ approaches infinity?
Apr 11, 2026
general
Cubic Hermite spline Derivative
I’m using the cubic Hermite spline to interpolate the position of a body as a function of time, here’s the formula: https://en.wikipedia.org/wiki/Cubic_He...
Apr 11, 2026
