updates
First and second derivative of a summation
Consider the function $f(\mu) = \sum_{i = 1}^{n} (x_i - \mu)^2$, where $x_i = i,\,i=1, 2,\dots, n$. What is the first and second derivative of $f(\mu)$?
Apr 18, 2026
Archive: Updates
updates
Difference between separable and linear? Differentials
My understanding was that a separable equation was one in which the x values and y values of the right side equation could be split up algebraically. I tr...
Apr 18, 2026
updates
Can a polynomial of degree 2 be non quadratic
By wikipedia: In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one o...
Apr 18, 2026
![What is the value of $e^{3i \pi /2}$? [duplicate]](https://news.conceivablytech.com/uploads/what-is-the-value-of-e-3i-pi-2-duplicate_720.jpg)
updates
What is the value of $e^{3i \pi /2}$? [duplicate]
When solving for the value, we know that $e^{\pi i}=-1$ . I am confused as to what is the right answer when you evaluate this.I am getting two possible an...
Apr 18, 2026
updates
Proof of the Euler Generalisation of Fermat's Little Theorem using modular arithmetic
Fermat's Little Theorem, in Fermat-Euler form, states that: if $\gcd(a,m)=1$, then $a^{\varphi(m)} \equiv 1 \pmod{m}$. Now, I've been asked to p...
Apr 18, 2026
updates
How can i solve this separable differential equation?
Given Problem is to solve this separable differential equation: $$y^{\prime}=\frac{y}{4x-x^2}.$$ My approach: was to build the integral of y': $$\int...
Apr 18, 2026
updates
Symmetry of polar equations
In your opinion how to show symmetry in polar equations without graphing. i thought of these methods :- converting to cartesian then test . check the peri...
Apr 18, 2026
![Expected value of a function of a random variable [duplicate]](https://news.conceivablytech.com/uploads/expected-value-of-a-function-of-a-random-variable-duplicate_720.jpg)
updates
Expected value of a function of a random variable [duplicate]
Let X be a random variable whose PDF is $f(x)$, and $g$ a function of random variable X. I want to prove that $$E[g(X)] = \int{g(x)f(x)dx} $$ I've pe...
Apr 18, 2026
updates
What does a graph of "A 7th degree polynomial equation with 4 imaginary roots" look like?
The question is "Draw a graph that possibly represents the following situation: A 7th degree polynomial equation with 4 imaginary roots." How would I draw...
Apr 18, 2026
updates
Why are power series centered around 0
I was wondering if there was any particular reason that power series are centred around 0. $$\displaystyle f(x)=\sum_{k=0}^{\infty}c_{k}x^{k}\qquad \text{...
Apr 18, 2026
