Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 103

Why is my value for the length of daylight wrong?

I was watching a YouTube video where it showed how length of daylight changes depending on the time of year, and I was curious and wanted to try calculating the...

Asked on 11/01/2021 by user525966

2 answer

Is this the right way of solving $frac{d}{dx}(sin(x)cdot x^2)$

I don't know much about theorems related to limits and I'm currently learning calculus from 3Blue1Brown's online series : Essence of Calculus. This example's generalization is what I'll use to...

Asked on 11/01/2021

1 answer

If$|f(x)-f(y)|le (x-y)^2$, prove that $f$ is constant

(Baby Rudin Chapter 5 Exercise 1)Let $f$ be defined for all real $x$, and suppose thatbegin{equation}tag{1} |f(x)-f(y)|le (x-y)^2end{equation}Prove that ...

Asked on 11/01/2021 by User31415

3 answer

How to evaluate $int _0^{infty }frac{ln left(x^3+1right)}{left(x^2+1right)^2}:dx$ without complex analysis

This particular integral evaluates to,$$int _0^{infty }frac{ln left(x^3+1right)}{left(x^2+1right)^2}:dx=frac{pi }{8}ln left(2right)-frac{3pi }{8}+frac{pi }{3}ln left(2+sqrt{3}right)-frac{G}{6}$$And its been proven here.But i'd like to know how to evaluate this...

Asked on 11/01/2021 by user809806

2 answer

Given an $ntimes ntimes n$ cube, what is the largest number of $1times 1times 1$ blocks that a plane can cut through?

This question is of recreation nature, but could be made more serious.Given a $3times 3times 3$ cube, what is the maximum number of small $1times 1times 1$ blocks...

Asked on 11/01/2021 by maomao

5 answer

Does the center of a perfect group not contain all elements of prime order?

Let $G$ be a finite perfect group (i.e. $G=G'$) and $Z(G)$ be its center. I don't know whether this statement is correct:There exists an element $x$...

Asked on 11/01/2021

3 answer

Intuition on spectral theorem

In the last month I studied the spectral theorems and I formally understood them. But I would like some intuition about them. If you didn’t know spectral theorems, how would...

Asked on 11/01/2021 by Eureka

3 answer

Question about finding roots of a polynomial and studying the nature

The number of real roots of the equation $1+frac{x}{1}+frac{x^{2}}{2}+frac{x^{2}}{3}+cdots+frac{x^{7}}{7}=0$(without factorial) isMy work Let,$mathrm{f}(mathrm{x})=1+frac{x}{1}+frac{x^{2}}{2}+frac{x^{3}}{3}+cdots+frac{x^{6}}{6}$ [Let, f has a minimum at $x=x_{0},$ where then $f^{prime}left(x_{0}right)=0$] ...

Asked on 11/01/2021 by user801681

1 answer

Integrate $frac{theta sin theta}{1+cos^2 theta}$ with respect to $theta$

Integrate :$$int_0^pi frac{theta sin theta}{1+cos^2 theta} dtheta$$I tried to do a substitution by letting : $u=cos theta implies du=-sintheta dtheta$ But I have a problem...

Asked on 11/01/2021 by user768934

4 answer

Zeno's Achilles & Tortoise - Where exactly is the proof wrong?

(For those who don't know what this paradox is see Wikipedia or the Stanford Encyclopedia of Philosophy.) Let us define $a_i$ and $b_i$...

Asked on 11/01/2021 by aman_cc

18 answer

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