An archived instance of a Calc III forum

Your favorite function

mark

(5 pts)

As students who’ve already learned mathematics through Calculus II, I assume that you all have a favorite function. Your first assignment is to tell us about it. Specifically,

Type out your favorite function using LaTeX syntax and
Include a graph of your favorite function.

Check out this post on formatting in the forum to see how to input stuff nicely into the forum.

audrey

My favorite function is f(x) = e^{-x^2}. Its graph looks like this:

By the way, I typed that in like so:

$f(x) = e^{-x^2}$

I created that graph using GeoGebra.

Jake

My favorite function is probably just a simple f(x) = \sin (x). I find it cool and scientific looking, yet kinda like a wave, plus you can use pi rather than just regular integers.

knguyen3

One of my favorite functions is the hyperbolic tangent activation function (or tanh). It is one of the popular activation functions in neural networks. Similar to a sigmoid function but having a better range (-1, 1).

\tanh(x) = \frac{e^x-e^{-x}}{e^x+e^{-x}}.

rstahles

My favorite function is f(x) = \vert sin(x^x)/2^{((x^x-pi/2)/pi)} \rvert. The graph of this function can be seen below:

Sara

My favorite function is r = 8\sin(4\theta) because I like that if you change the number in the parentheses it changes the number of petals the little flower has.

Colby_Howell

My favorite function varies frequently, and at the moment it is f(x) = \sin(x) - \cos(x) + \tan(x).
I enjoy the repetition of the two lines it produces, and also that when zoomed out far enough it becomes a wall of color on desmos.
here is the graph:

jlajcin

My favorite function is f(x)= (cos(x^2)+x)^2 . It’s pretty cool on how it looks which is:

Samwise

My favourite function is incredibly simple, but it’s my favourite because of how easy it is to integrate. Whenever I have to take derivatives or antiderivatives, I’m relieved to see f(x)=e^x.

ScottLashley

My favorite function is f(x) = 1/x. I like how 1/x is the inverse of x and the left side of the graph is the reciprocal of the right half

inverse function

mbanawan

My favorite function is the base function of a circle because of how the center coordinates are the inverse of what you put in the function. x+1 means -1 x coordinate, etc.

1= (x-1)^2+(y+2)^2

scaldwe4

My favorite function is. I think its cool because of the asymptotes on the x and y axis.

f(x) = cos(x)/sin(x) + tan(x)

mhernan5

My favorite function is
x^2 +(y-1/2|x|^(1/2))^2=1 . I found this when messing with making circles last semester in calc 2. This is how it looks.

dspivey

My favorite function is f(x)= sin(99x) because I like the comb like look of the curves.

mparog

My favorite function is f(x) = x * sin(x) and the graph looks like this:

nhaley

My favorite function is f(x) = tan(\frac{1}{x}). Its graph looks like this:

Alexander_The_OK

One of my favorite functions is f(x)=x^4+y^4-x^{-2}
Because I think it looks cool.

whardin3

My favorite function is \ln(x) purely for the fact that it is rather easy to derive from, since it’s just 1 over the value inside the function, which is a really nice breath of fresh air when tackling very complex problems (except when you end up having multiple \ln(x), which makes it VERY interesting to formulate the denominator correctly.

nfitzen

My favorite function is simple; it’s just \ln(x). I like it because it’s used everywhere similar to e^x, particularly in number theory and statistics.

geogebra_screenshot

myost

my favorite function is

f(x)=sin^2(x)

Screen Shot 2022-08-15 at 1.41.11 PM