general
Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$
I'm having trouble computing the integral: $$\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx.$$ I hope that it can be expressed in terms of elementary...
Apr 19, 2026
Archive: General
![Infinite powers of aleph-omega [duplicate]](https://news.conceivablytech.com/uploads/infinite-powers-of-aleph-omega-duplicate_720.jpg)
general
Infinite powers of aleph-omega [duplicate]
The book of Thoms Jech on set theory mentions some equalities involving $\aleph_{\omega}$: $\aleph_\omega^{\aleph_1} = \aleph_\omega^{\aleph_0} \cdot 2^{\...
Apr 19, 2026
general
What is the difference between an infinite set of 1 dollar bills and an infinite set of 20 dollar bills?
Even though both sets approach infinity at different increments, do they eventually approach infinity at the same value at the same degree? Or is the seco...
Apr 19, 2026
general
Finding Tangent Line Using Limit Definition
I'm supposed to get the equation of the tangent line to the graph of $f(x)= \frac{8}{x}$ at the point $(2,4)$. I started with $$\frac{\frac{8}{x+h} -...
Apr 19, 2026
![Find the value of y [closed]](https://news.conceivablytech.com/uploads/find-the-value-of-y-closed_720.jpg)
general
Find the value of y [closed]
Given: $$x\frac{dy}{dx} = \cot y - \csc y \cos x, \ \ \lim_{x \to 0}y(x) = 0,$$ find $$y\left(\frac{\pi}{2}\right)$$
Apr 19, 2026
general
Why is the conjugate of a function always convex?
The conjugate of a function $f$ is given (for some $y \in \operatorname{dom}(f)$) as: $$f^*(y) = \sup_{x \in \operatorname{dom}(f)}\left(y^Tx - f(x)\right...
Apr 19, 2026
general
Which symbol can be used to refer to identity matrix?
$I$ is commenly used as a notation of identity matrix. I am wondering is there any notation else for identity matrix?
Apr 19, 2026
general
A complete ring with respect to an ideal
I would like to know what does it mean to say " a ring $R$ is complete with respect to some ideal $I \subset R$. Is it like, we define a metric by saying ...
Apr 19, 2026
general
What is the definition of "Smallest Set" used in Linear Algebra?
In Axler's Linear Algebra Done Right the theorem given is Suppose U1,…,Um are subspaces of V. Then U1+⋯+Um is the smallest subspace of V containing U...
Apr 19, 2026
general
How to calculate the upper and lower Riemann sums with respect to this particular partition P?
I am having some trouble with this practice problem that is: Let $f(x) = 2x$ on $[0,3]$. Calculate the upper and lower Riemann sums with respect to the pa...
Apr 18, 2026
