Questions regarding the plotting or graphing of functions. Questions about graphs with vertices and edges should use the (graph-theory) tag instead.

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4
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109 views

Graphs of interesting integrals of the form: $\int \sin^a(x^a)\cos^a(x^a)$

Here are a few graphs of the form:- $$\int \sin^a(x^a)\cos^a(x^a)dx$$ Where $a$ is an even, positive integer. $a = 2$ $a = 4$ $a = 6$ Now, a few graphs of the form:- $$\int ...
4
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136 views

How do you call functions that fulfill $f(x)=\pm f(\pm 1/x)$?

A function $f(x)$ that fulfills $f(x)=\pm f(-x)$ is called (a)symmetric even/odd. How do you call functions that fulfill $f(x)=\color{blue}\pm f(\color{red}\pm 1/x)$? ...
3
votes
0answers
18 views

How does emergent oscillation appear in this animation of concentric circles?

I made this animation and I barely understand it. http://bl.ocks.org/tophtucker/500d2a010105cfcc87db It's a bunch of concentric circles with exclusion compositing. The radius of the ...
3
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39 views

Plotting a 4D Dynamical System

Suppose I have a 4D dynamical system. Each axis has a fixed point, and there are orbits connecting the fixed points. It looks something like this: Each $Q_i$ is a fixed point on each axis of a ...
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130 views

Visualising surface integrals

For a current problem I am working on, I have run into angular surface integrals, i.e. the differential solid angle $\text{d}\Omega$. Specifically the surface integrals are defined by ...
3
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81 views

Plot implicit equation in sub-quadratic time complexity

It is fairly straightforward to plot an explicit equation such as $y=x^3+3x^2+2x+5$ in linear time, because you can just iterate through all $x$ in your graphing space and use the equation to ...
3
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99 views

Properties and representations of the the rescaled complementary error function $\mathrm{erfcx}{z}$

Consider the rescaled complementary error function: $$ \mathrm{erfcx}(z) = {e^{z^2}} \left( {1-\mathrm{erf}(z)} \right) $$ $z \in \Bbb{C}$ which also has the following integral representation: $$ ...
3
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64 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
3
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429 views

Recognizing subadditivity

Let $f: (0,\infty) \to \mathbb{R}$ be some continuous function. We say that $f$ is subadditive if the bound \begin{align} f(x+y) \leq f(x) + f(y) \tag{1} \end{align} holds. I was attempting to ...
3
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201 views

Sketching the graph of a function

How would I sketch the graph of the following function. Sketch the graph of a function satisfying the following conditions $f(1)=2$ $f(-1)=f(3)=-1$ $f'(1)=0$ $f'(x)>0$ for all $x<1$ ...
2
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29 views

Why does this odd glitch exist with graphing programs?

In Grapher on Mac and the TI-84's built-in graphing program, there is a problem with imaginary numbers. If I input $ i\sqrt {x}$, the graph ends up looking like this, even though it ought to look like ...
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61 views

What would the graph of $y=\sin(\log x)$ look like?

What would the graph of $y=\sin(\log x)$ look like? So far I have dawn the conclusions : At $x=1$ $y=0$ The graph never touches $x=0$ ($y$ axis) The maximum is attained at $x = \exp(\pi/2)$
2
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30 views

Is my graph correct?

My problem told me that: Let $S$ be the surface described by the equation in cylindrical coordinates $z = r^2$, and the inequality $0 ≤ z ≤ 4$, oriented such that the unit normal vector points ...
2
votes
0answers
78 views

Fourier Series of the batman equation

I want to represent the batman equation as a Fourier Series. (I got the equation here : Is this Batman equation for real?) But a part of it is an ellipse and when I tried to calculate an the integral ...
2
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0answers
52 views

Graphing the derivative from a graphed function

For the graphs of $f(x)$ make a sketch of the graph $f'(x)$ Here are the sketches I have so far. The graphs on the top row are the original functions. Did I graph these correctly?
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70 views

Why is the graph of 4 nodes and 2 edges not self-complementary?

I am having some trouble seeing why a graph of 4 nodes and 2 edges is not self-complementary such that G is isomorphic to G bar (G complement) (please see the attachment below). I know that the number ...
2
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263 views

Differential Equation Direction field

What i want to achieve: I want to plot the direction fields of the following three differential equations: 1. Malthusian growth model: $p'(t)=\lambda*p(t)$ with $\lambda=1$ and $p(t)=t$ 2. Linear ...
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0answers
74 views

Is there a way to graphically show that a solution is the minimum or stationary solution to a functional?

I'm looking for the functional analogue to the visual representations of function optimization you most commonly see. To illustrate, if we have some function: $$ f(x) = (x-1)^2+1 $$ We can look at ...
2
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0answers
189 views

Math software for plotting phase portraits

I'm looking for math software which is possible to plot phase portraits for ODE and systems of differential equations. Is there a software which can create not only simple 2D phase portrait plots but ...
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47 views

Plot histogram and density function

I need to plot a histogram for the data: ...
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0answers
56 views

$x^{y}=y^{x}$ Intersection Question

I'm looking at this problem, $x^{y}=y^{x}$ and the question is to find the point of intersection of the two curves that form a solution set. I understand how to find the point of intersection using a ...
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0answers
78 views

Should a “good” equation divide the plane?

At the question Is there any equation for triangle? (MSE) the answer given by Henning Makholm received the most upvotes. Therefore let's define the following triangle function $H$ with (a,b,c) the ...
2
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0answers
99 views

Using Graphs Changes the Solutions for Diophantine Equation? Imperfection of Graph?

Solve the Diophantine equation $$x^2+4y^2=z^2$$ The problem here is that I derived solutions using two different methods, and the both solutions do satisfy the given equation yet they are ...
2
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0answers
162 views

how to choose point spacing to approximate a parametric curve using line segments?

Suppose I have a parametric equation for a curve $\vec{r} = f(t)$, which I wish to draw using line segments between some set of points at times $t_0, t_1, t_2,$ etc. If I want to achieve a given ...
2
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0answers
334 views

Find a function (curve fitting) for given values

I am trying to assign scores for URLs based on their view counts. I have about 300,000 URLs. In a two-day interval, only 1 URL got more than 5000 views 8 got between 1,000 and 5,000 views about 500 ...
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0answers
215 views

Ellipse radius interpolation with different radiuses

I am writing a library for graphical LCDs and I want to incorporate a function to draw a circle on the screen. I have already succeeded in drawing simple circles, however, I want to be able to pass a ...
2
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0answers
78 views

planarity of graph as a consequence of its flow

Is it possible to distinguish planar and non-planar graphs (networks as a matter of fact) by flows? That is, is there a flow criterion for a graph being planar or not?
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217 views

My solution is right and the book is wrong (parabolas) or did I misunderstand it?

Find the equation of the parabola with the vertex at the origin; directrix 2x = 3 So what I did is, find the equation of the directrix $$x = \frac{3}{2}$$ and then because its the directrix, the ...
2
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0answers
282 views

how to obtain state space diagram and state space model for transfer function

How do we obtain the state space diagram and state space model for transfer function for example the question is given How to draw state variable diagram for the given transfer function ...
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0answers
11 views

How to calculate a time estimate and plot it?

I recently made a website for a game's community. The game basically has an online dragon which people can fight. Each fight chips off a little bit health. On the next encounter with the dragon, ...
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15 views

Homogeneity of $f(x,y) = \frac{3x^2y}{x^2+y^2}$

Regarding my previous question about the function $f(x,y)$ somebody claimed that $f(ax,ay)=af(x,y)$ is only true for "homogeneous" $x$ and $y$. Does anyone know what "homogeneous" means in this ...
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0answers
12 views

Determining function of Graph

Looking through some notes on numerical computation I came across the following graph: I know this is a longshot, but I'm not incredibly mathsy and would like to know what kind of a function this ...
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0answers
37 views

How can I plot the complex function in 2D?

My function: $$sin(wt-jT) \tag{1}$$ where $j$ - complex unit, $T=0.1,\ w=8 \pi,\ t=[0,0.01,0.02..100]$ I transform it to function with real arguments: $$\sin(wt)\cosh(T)+j\cos(wt)\sinh(T) ...
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0answers
19 views

From current plot $y=f(x)$ get plot $dx/dy$ vs $y$

I have a plot $y = f(x)$ where $y$ is voltage and $x$ is capacity. Now I want get from this graph the $dx/dy$ vs $y$ plot. How can I get this new graph?
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23 views

rotation of spherical surface in spherical coordinates

I need to plot a spherical surface in computer (like the surface of a lens). I know the normal vector (as an example, say $\ n=(1,2,3) $) of this surface and it originates from the centre of the ...
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0answers
33 views

How to Trace a Real-Life Flower Using Polar Equations?

Here is the flower I'm trying to trace: $\hskip2cm$ How can I trace this flower using polar equations? I currently have the formulas \begin{align} r_{1}&=1.75\sin(10\,\theta + 18) +3\\ ...
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0answers
35 views

Why use ln-ln plot in proportional hazard test?

I recently study survival analysis since couple of months ago, and there is one question which makes me curious. a simple and (maybe) a stupid question. Why do we prefer to use ln-ln survival curve ...
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31 views

Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.

Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.Here $\text{frac}(x)$ is a fractional part function. ...
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0answers
16 views

Picturing/Graphing (quasi-)concave/convex functions?

I understand the definitions, and can do work with them, but when I try to picture them I get confused (picture simple concave/convex functions that is, not some very complex ones obviously). ...
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0answers
19 views

Analytic formula for parameterizing the below family of curves

I'm trying to find an analytic formula for a curve that can look like any of the curves below depending on one or more parameters. My initial thought was to use exponentials, something that might ...
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0answers
29 views

What kind of topological sorting exists in graph theory and what are their graphic plotting?

I know that there is at least two kinds of topological sorting: "by rank" and by"level" a level of a vertex is the maximal length of a path with x as an extremity. a rank of a vertex is the maximal ...
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0answers
13 views

Number of hyperbolae from 3 points with a known absolute difference in distance

In GPS, measuring the correct distance to satellites is not possible due to clock errors in the receiver (what you measure is called a psuedo range because it is based on incorrect time which ...
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0answers
35 views

Parametrization of helicoid like surface for Faraday's law of induction of a solenoid?

I want to visualize with mayavi a possible surface for Faraday's law of induction in the electrodynamics of a solenoid. I.e. something like a helicoid with a smooth transition to a rectangular area, ...
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63 views

Does anyone recognize this graph?

It's a plot of the following: Let $$f_{(n)} = \frac{np_n}{(p_1 + \ldots + p_n)}$$ so that $$g_{(n)} = \left|\space f_{(n)} - f_{(n-k)}\right| $$ where $n > k$ and $k = 5$ in this example. For ...
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0answers
53 views

parsimonious definition of a zig-zag function between two bounds

Suppose I have some strictly increasing function $f:[0,b]\to[0,b]$ with $0<b<1$, $f(x)<x$ and $f'(b)=\frac{1-f(b)}{1-b}$ (i.e. tangent to the secant line to $(1,1)$). Now imagine a 'tunnel' ...
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0answers
43 views

Create log-normal on y axis?

I currently have a graph with log numbers on the x-axis and the y-axis goes from 0-100. How can I get it to I guess log normal y-axis as shown in the picture below? Thank you for your help!
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0answers
74 views

Determine null, extreme and inflection points of function $f(x)=\frac{x+e^x}{x-e^x}$

This function has a null point, but I can't compute it from equation $f(x)=0$ which gives $$\frac{x+e^x}{x-e^x}=0$$ $$x+e^x=0$$ How to compute this equation? Extreme points can be computed from ...
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0answers
43 views

Sketch the level curves of the function $f(x,y) = (x+y)^4$

My attempt: Let $$z = (x+y)^4 \iff \pm \sqrt[4]{z} = (x+y)$$ Since $z$ is a constant, $\sqrt[4]{z}$ will also be a constant. $$(x+y) = \sqrt[4]{z} = c \iff y = -x + c$$ So the contour plot will ...
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38 views

Matlab, Extracting Particular Values from an Excel File

If I have a table of values in Matlab ( here I have a 40k rows, and about a dozen columns), how can I read only particular values from each row? My goal is to extract some of the values from each row, ...
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38 views

Could someone explain to me why the range of the graph is R\(0,5]

I am trying to help my brother with his exam preparations, and we came across this question and found the answer a little confusing. Here is the graph and the range, taken from the answers page of the ...