A service that has several calculators and teaching material for Mathematics, with its most prominent feature being a graphing calculator that is available as an app and on a website.
Questions tagged [desmos]
100 questions
24
votes
1 answer
How to use AND condition in Desmos
Sorry maybe it's not typical mathematics question, but Desmos is very helpful in solving and testing mathematics issues, so maybe anyone could help me.
I can't figure it out how to use AND condition in Desmos
For example to make OR you can just use…
pajczur
- 523
14
votes
1 answer
Why does this desmos plot of the integral of $\sqrt{1+e^x}$ have these discontinuities?
I computed the integral of $\sqrt{1+e^x}$ by hand and got
$$2\sqrt{1+e^x} + \ln\left(\sqrt{1+e^x} - 1\right) - \ln\left(\sqrt{1+e^x} + 1\right) + C,$$
or
$$2\sqrt{1+e^x} + \ln\left(\frac{\left(\sqrt{1+e^x} - 1\right)^2}{e^x}\right) + C.$$
But when I…
Zhiyuan Liu
- 371
14
votes
3 answers
Express "if true, then 1 else 0" in a formula suitable for Desmos calculator
In programming, often the value of True is also 1, and False is 0.
This means that:
(x>5)*4
will return 4 if x is greater than 5 (because (x>5)==1), else 0.
I need to accomplish a similar thing using mathematical operators (no piecewise functions,…
user191074
12
votes
3 answers
Integral concerning the floor function
I have a problem with the following integral:
$$
\int_{1}^{\infty}\frac{\sin\left(\frac{\pi}{2}\{x\}\right)^{[x]}}{[x]}\cos\left(\frac{\pi}{2}\{x\}\right)\,dx
$$
where $[x]$ is the floor function and $\{x\}:=x-[x]$. I tried to solve it using the…
Davide
- 740
7
votes
2 answers
$\frac{\max(1,xy)}{y} = x$: Did I just create a fractal?
https://www.desmos.com/calculator/6hfyqc6ks9
Did I just create a fractal? Again, the function is $\frac{\max(1,xy)}{y} = x$.
Even uncannier version, from the alternative form with "sgn" that Wolfram provided:…
Josh
- 477
6
votes
4 answers
Why do the peaks of $f(x)=x^{\cos(x)}$ approach $g(x)=x$?
I was just messing around in desmos when I came across an interesting function, $f(x)=x^{\cos(x)}$. I noticed that the peaks were getting closer and closer to the inputted $x$ values, while the troughs approached $0$. So I went and found the…
R. Reed
- 355
5
votes
0 answers
Desmos not plotting the obvious inequality correctly?
I was checking the subadditivity of the function $f\colon x\mapsto \min(1, x)$, i.e., whether $f(x + y)\le f(x) + f(y)$ and was expecting that the entire first quadrant would be colored. However, the following was outputted:
But clearly, for…
Atom
- 4,620
5
votes
2 answers
Efficient Formula for $\zeta(3)$
I was messing around with Desmos to find an exact form for $\zeta(3)$ and was using the following triple integral form:
$$
\zeta(3)=\int_0^1{\frac 1 z\int_0^z{\frac 1 y\int_0^y{\frac 1 {1-x}}}}dxdydz
$$
I set it to $a$ in Desmos, and…
Andrew Sotomayor
- 436
5
votes
1 answer
Ellipse bounded between two lines and a circle
Given two circles with radii $\beta$ and $\beta^{-1}$, where $\beta\geq1$. Also, given two lines $y=x\tan\alpha$ and $y=-x\tan\alpha$, where $\pi/2>\alpha\geq0$. I am interested in all ellipses with center at $(k,0)$ that are bound between these two…
Lee
- 1,978
4
votes
1 answer
Why does Desmos not render graphs like this properly?
I was trying to show some students the graph of $y=4- \ln (2-x)$ today on Desmos.
Unfortunately we can see from the picture below that the graph does not render correctly around the asymptote and appears to 'stop' at around $y=40$. This same…
PhysicsMathsLove
- 3,270
4
votes
5 answers
Discrepancy in definite integral $\int_{0}^{2\pi}\frac{1}{10+3\cos x}dx$ using Desmos
I was trying to calculate the following definite integral of a function $f(x)$:
$$\int_{0}^{2\pi}\frac{1}{10+3\cos x}dx$$
After some effort, I managed to find the following antiderivative:
$$F\left(x\right)\ =\…
Zacky
- 41
4
votes
2 answers
How would one describe $k$ iterations of $\cos(n)$?
What function would one use to describe $k$ iterations of $\cos(n)$? I'm pretty sure that the function would be a damped sine wave (as can be seen in the curve fit equation I wrote in the third row), however the actual formula is probably quite…
Josh
- 477
4
votes
1 answer
Why ambiguities show up analytically and not graphically?[Limits]
I'm sorry if I sound naive but I have recently studied the topic of limits in high school and didn't understand something.
I understand that we need limits for determining undefined values like $\frac{0}{0}$, ∞/∞ ,1 raised to ∞ etc,but why do we…
Kashi
- 115
3
votes
2 answers
Weird discrepancy in the calculation of an integral.
Integral in question, and its answer
The integral $$\int_{0}^{1000} e^{\left\{ x \right\}}\, \operatorname{d}x$$
where $\left\{\cdot \right\}$ is the fractional part function, evaluates to $1716.02$ in Desmos, which should THEORETICALLY be equal to…
sachyrus
- 43
3
votes
0 answers
How should I keep arc length equal between multiple points on a parametric curve?
I made this thing in desmos:
https://www.desmos.com/calculator/na9sehjskk
The distance between points changes depending on the speed of the points. Is there a way to keep the distance between them equal at all times?
I tried changing the difference…
