I'm trying to prove the derivative of $\sqrt{x}$ using geometry. So far I've created a square with area $x$ and side lengths $\sqrt{x}$. The der...

How can I show that a circle that is tangent to $x$-axis and $y$-axis has radius $R$ and center $(R,R)$ using algebra? So I have this concept about it. Si...

Examine whether $b: \mathbb R ^3 → \mathbb R^3 $ is a vortex field and determine a vector potential $a$. $b=\begin{pmatrix} 4x^4y^3z^2-3x^4z^2 \\ -4x^3y^4...

How can I prove this? Should I take $x$ and $x+2$ or not ? I am confused.

In my class 10 book I got to know a formula of finding mode in grouped frequency distribution table. That formula is L+ (f1-f0)\ (2f1-f0-f2)× H Where, L i...

Proposition 21. Let $\varphi$ be the Cantor-Lebesgue function and define the function $\psi$ on $[0,1]$ by $$ \psi(x) = \varphi(x) + x \quad \text{for all...

I have been asked to determine whether- $h : \mathbb{N} \rightarrow \mathbb{N}$ defined by $h(x) = x^3$ is injective, surjective or bijective. And why?

In part (a), I calculated that s(t) = $\int_0^t \! (\frac{t^2}{2} + 2t) \, \mathrm{d}t$ = $t^2/2 + 2t$ I'm unsure how to solve part (b). My attempt i...

For example, suppose we have the following two problems that we'd like to find the Laplace transform of: $f(t) = \begin{cases} 1, & t \lt 2 \\ 0,...

Translate the following argument into symbolic form. State clearly what each of the propositions are I walk and I cycle and I run. If I do not stay at hom...