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Your favorite function
What is your favorite function? Enter it in nice, typeset mathematics and plot it, together with the line [imath]y=x[/imath].
Comments
My favorite function is the same as my Dad's! It's:
[dmath]
f(x) = e^{-x^2}.
[/dmath]
The graph looks like this:
Ayy my favorite function is:
[dmath]
f(x)=e^{ix}
[/dmath]
My beloved function is for the Lorentz factor because it is so useful for my favorite frame of reference.
[dmath]
\gamma = \frac{1}{\sqrt{1- \frac{v^2}{c^2}}}
[/dmath]
https://www.desmos.com/calculator/qgilurylz6
My favorite function is:
[dmath]
y=\ln (n!)
[/dmath]
My favorite function is:
[dmath]
f(x)=\sin(x+f(x))
[/dmath]
The graph looks like this:
My favorite function is just the natural exponential function is the humble natural exponential function, solely for the reason that its derivative is itself.
[dmath]
f(x) = e ^ x
[/dmath]
The graph looks like this:
My favorite function is [dmath]f(x)=\sin \frac{1}{x}.[/dmath] The rate of oscillations increase without bound as x approaches zero, which results in the neat springy shape seen in the linked image.
My favorite function is
[dmath]
f(x)=x^3.
[/dmath]
The graph to this function looks like this:
https://www.desmos.com/calculator/lmavj1l9ib
My favorite function is
[dmath]
f(x) = sin(x) + x
[/dmath]
The graph to this function looks like this:
https://www.desmos.com/calculator/ohk5s6uvah
One of my favorite functions is:
[dmath] r =2sin(8.5theta) [/dmath]
where the coefficient of theta can be changed to create all kinds of beautiful flowers!
Graph: https://www.desmos.com/calculator/jbpa4gdxms
My favorite function is:
[dmath] f(x)=cos(3x+3)! [/dmath]
The graph looks like really long teeth!
Graph:
Lately I have been very fond of this function:
[dmath] f(x)=3sin(ln(θ^{2}+1)) [/dmath]
Here is what it looks like:
[dmath]
f(x)=e^{-x^3}
[/dmath]
* It looks like this! I find it to be an accurate indicator for my GPA throughout the semester with respect to time!
*
My favorite function is
[dmath]
f(x) = x^{2}
[/dmath]
specifically in relation to its derivative, 2x. "Calculus" is a word that conjures up great fear in the general public. It's uttered in hushed tones and is often met with a grave silence while those who hear it respond with the stone faced seriousness of a soldier re-living the horrors of war. But if you can look at x^2 and decide that for your own purposes that you want it to be 2x now, you're doing calculus. Easy!
This is what it looks like:
A function I like is:
[dmath]f(x) = \log(x)+\sin(x^{3})[/dmath]