updates
Parametric form of a line in 3D
I always get confused when i see an equation of line Given in a shape like r :2x=y=2-2z How can i write it in a parametric form Like r: $$ \left\{ \begin{...
Apr 20, 2026
Archive: Updates
updates
Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$
Problem: Show that $$\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}.$$ My progress: The problem before this one had me find the Taylor series for $\ln(1-x)$ ...
Apr 20, 2026
updates
I need help understanding the formal definition of a limit
I had been taught the formal definition of a limit with quantifiers. For me, it is very hard to follow and I understand very little of it. I was told that...
Apr 20, 2026
updates
Finding the limit, multiplication by the conjugate
I need to find $$\lim_{x\to 1} \frac{2-\sqrt{3+x}}{x-1}$$ I tried and tried... friends of mine tried as well and we don't know how to get out of: $$\...
Apr 20, 2026
updates
Finding the inverse of a rational function (quadratic dividend and divisor)
I've solved functions where it has a linear dividend and divisor only before and this is pretty new to me. I tried solving this by using what I'...
Apr 20, 2026
![How to calculate the square root of a number? [duplicate]](https://news.conceivablytech.com/uploads/how-to-calculate-the-square-root-of-a-number-duplicate_720.jpg)
updates
How to calculate the square root of a number? [duplicate]
By searching I found few methods but all of them involve guessing which is not what I want. I need to know how to calculate the square root using a formul...
Apr 20, 2026
updates
Finding the asymptotes of a general hyperbola
I'm looking to find the asymptotes of a general hyperbola in $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ form, assuming I know the center of the hyperbola ...
Apr 20, 2026
![Proof for hyperbolic trigonometric identities [closed]](https://news.conceivablytech.com/uploads/proof-for-hyperbolic-trigonometric-identities-closed_720.jpg)
updates
Proof for hyperbolic trigonometric identities [closed]
I've been studying hyperbolic functions and was wondering where the following two identities were derived from: $$\sinh(x) = \frac{e^{x}-e^{-x}}{2}$$...
Apr 20, 2026
updates
Can we call surjective and injective onto and into?
How often is terminology introduced or changed in the math community? I know that John Conway did it all the time - but he was distinguished and often nam...
Apr 20, 2026
updates
Is a symmetric real matrix similar to a diagonal matrix through an orthogonal matrix?
Definition Two matrices $A$ and $B$ are said similar if there exist an inverible matrix $P$ such that $$ B=PAP^{-1} $$ Definition A square matrix $A$ is s...
Apr 20, 2026
