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I have to show that the recursive sequence given by $$ b_1 = 1, ~ b_{n+1} = b_n + \frac{1}{(3 + (-1)^n)^n} $$ converges. I can show its convergence by sho...
I'm trying to self-learn math and I'm starting with naïve set theory. The only problem is that the book I'm using lacks a solution textbook...
I want to know if a 3D spiral, that looks like this: can be approximated to any sort of geometric primitive that can be described with a known equation, l...
What is derivative of $f(x)=\left(\dfrac{\sqrt[3]{x^2+2x}}{x^2-x}\right)^3$ at the point $x=2$? $$1)-\frac34\qquad\qquad2)-\frac54\qquad\qquad3)-\frac52\q...
I searched in Google for the definition of Platonic solid, and I found: A platonic solid is a polyhedron all of whose faces are congruent regular polygons...
![Distance between the foci [duplicate]](https://edu.smbbmcl.edu.pk/uploads/distance-between-the-foci-duplicate_720.jpg)
A circle has the same centre as an ellipse & passes through the foci FI & F2 of the ellipse, such that the two curves interseet in 4 points. Let &...
$$y=\frac{2}{3}x^{\frac{3}{2}}+\frac{3}{2}x^{\frac{2}{3}}+1$$ Find the tangent line to the curve at $x=1$. I have taken the derivative of $y$ which was $$...
According to Wikipedia: Let C and D be categories. A functor F from C to D is a mapping that associates to each object $X$ in C an object $F(X)$ in D, ass...
I understand that: 1.Setting a boundary condition of the type $$u(x_0,t)=0$$ means that the wave will reflect and change sign. 2.Setting a boundary condit...
Text pasted from Thomas Finney Calculus book here: "Infinite intervals are closed if they contain a finite endpoint, and open otherwise. The entire real l...
