Mathematics

Questions tagged [desmos]

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.

102 questions
25
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
  • 533
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
  • 1,106
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
  • 2
  • 7
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
2 answers

Why does Desmos show $x=3\pi/2$ as a solution to $\tan x+\sec x=2\cos x$ even though the left-hand side is undefined there?

The main question was how many values of $x$ satisfy the equation $\tan x+\sec x=2\cos x$ in the interval $[0,2\pi]$ Solving for $x$ gives two valid solutions (namely $\frac\pi 6$ and $\frac{5\pi} 6$ ) and one invalid solution (namely…
Noor
  • 1,069
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
  • 4,718
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 evaluated: $$…
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…
Lee
  • 1,988
  • 13
  • 20
4
votes
1 answer

Is there a way to label points in 3D Desmos?

So I am working on making a cube in Desmos 3D with labeled vertices. If anyone would like the link to the Desmos 3D graph, here it is . The only problem is, I am unable to label the vertices for some weird reason, when I put down a point, such as at…
CrSb0001
  • 2,844
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
  • 3,366
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
  • 43
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
  • 2
  • 7
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
1
2 3 4 5 6 7