general
Comparing Square Roots
How do you compare square roots? Of course, the positive square root of 49 is greater than the positive square root of 36. However, what if you were to ha...
Apr 18, 2026
Archive: General
general
How to find the derivative of the function $y=5^{-1/x}$?
$$y=5^{-1/x}$$ Help would be so greatly appreciated :] It's another homework problem...I unfortunately was not present during the lecture for these t...
Apr 18, 2026
![$\lim_{x \rightarrow 0} [\frac{\arcsin x}{x}] = 1$, [] is floor function.](https://news.conceivablytech.com/uploads/lim-x-rightarrow-0-frac-arcsin-x-x-1-is-floor-function_720.jpg)
general
$\lim_{x \rightarrow 0} [\frac{\arcsin x}{x}] = 1$, [] is floor function.
Prove that $$\lim_{x \rightarrow 0} \left[\frac{\arcsin x}{x}\right] = 1$$ and $$\lim_{x \rightarrow 0} \left[\frac{\arctan x}{x}\right] = 0$$ where $[\,]...
Apr 18, 2026
general
Why does dividing a polynomial by $x-a$ give the same quotient as evaluating it at $x=a$ using synthetic division?
I know synthetic division is a table representation of the calculations that occur when evaluating a polynomial in Horner's form at some $x$ value ($...
Apr 18, 2026
general
How to interpret "computable real numbers are not countable, and are complete"?
On page 12 of this (controversial) polemic http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf Wildberger claims that Even the "computable real numb...
Apr 18, 2026
general
Categories of mathematics
I am interested in understanding how mathematics is divided into many categories, such as what categories are particular cases of what, what categories do...
Apr 18, 2026
general
How do I mathematically represent the faces of a die
If I were to represent the sides of a dice as a vector formula, what would that formula be? For example, a 6 sided die whose center is at 0,0,0 would be 1...
Apr 18, 2026
general
The range of sum/difference/product/quotient of two functions is the intersection of the ranges of the individual functions
Find out the range of $x^{\frac{1}{3}}+\sin 2x$ Since the range of the function $\sin2x$ is $[-1,1]$ and the range of the function $x^{\frac{1}{3}}$ is $R...
Apr 18, 2026
general
Number of ways to get 3 groups of 5 people each
i have been thinking about this problem and cant get the answer. Can you please help me solve it? There are 22 people and we have to make 3 groups (Financ...
Apr 18, 2026
general
Integration by parts $ \int \sqrt{x-x^2} dx $
I have to integrate $$ \int \sqrt{x-x^2} dx $$ The answer on my textbook is $ \frac 14 \left( \arcsin(\sqrt x)-(1-2x)\sqrt{x-x^2} \right) $ but I want to ...
Apr 18, 2026
