general
Phase line - differential equations..
For the differential equation: $$ y' = y(y+2) + 4 $$ I expanded it to: $$ y' = y^2 + 2y + 4 $$ I am asked to draw a phase line, and draw some ty...
Apr 16, 2026
Archive: General
![How do calculators calculate the value of trigonometric functions? [duplicate]](https://news.conceivablytech.com/uploads/how-do-calculators-calculate-the-value-of-trigonometric-functions-duplicate_720.jpg)
general
How do calculators calculate the value of trigonometric functions? [duplicate]
I have an obsession about trig functions. I find them to be so mysterious, because I really don’t understand calculus (other then trying to make sense of ...
Apr 16, 2026
general
How do I determine if measurements given for a triangle will produce one, two, or no triangles?
Example: a=7, c=28, A=12º Here is what I have so far.
Apr 16, 2026
general
A step function is right continuous with left limits
What does it mean that the characteristic function $f(x)=1_{[b \le x \lt \infty]}$ is right continuous with left limits? Here $x ,b \in \mathbb{R}$.
Apr 16, 2026
general
Understanding the unbiased estimator
I am having a hard time understanding what an estimator actually is (I miss the intuition.). The definition (for unbiased estimator) is as follows: $T$ is...
Apr 16, 2026
general
Limits indeterminate & undefined form
Preface: I'm a calculus student who's a bit frustrated because limits seem like the foundation of calculus and seems full of contradiction. If y...
Apr 16, 2026
general
Is there a symbol for "taking a derivative of something"?
When presented with an equation, say, $y=5x^3+7x^2+4x+9$, you can write on the second line, $\frac{dy}{dx}=15x^2+14x+4$. Similarly, $f(x)=5x^3+7x^2+4x+9$ ...
Apr 16, 2026
general
Woodbury Matrix Inversion
I am trying to invert a matrix using Woodbury identity. The inversion using Cholesky decomposition has the following pseudo-code: For $t=1,2,...$ $(1)\;\;...
Apr 16, 2026
![Convergence of the alternating $p$-series $\sum_{n\ge1} \frac{(-1)^{n-1}}{n^p}$ [closed]](https://news.conceivablytech.com/uploads/convergence-of-the-alternating-p-series-sum-n-ge1-frac-1-n-1-n-p-closed_720.jpg)
general
Convergence of the alternating $p$-series $\sum_{n\ge1} \frac{(-1)^{n-1}}{n^p}$ [closed]
Assuming $p>0$, we consider the $p$-series $$ 1-\frac{1}{2^p}+\frac{1}{3^p}-\frac{1}{4^p}+\cdots $$ For what $p$-values is the series convergent? For w...
Apr 16, 2026
general
How to find the limit of recursive sequence?
Suppose $a_0 = 0$, $a_1 = 1$, and $$ a_{n+1} = a_n+2 a_{n-1}$$ if $n \ge 1$. Find $$\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}$$ Usually, what's th...
Apr 16, 2026
