Tagged Questions

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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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 $x = \exp(\pi/2)$
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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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evaluating positive and negative regions for a simple compound function

I'm trying to understand how to analytically determine the regions where $y_1 \lt y_2$. If I set the functions equal to each other it yields $x=14$ which is true for that point but, as you can see ...
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How to plot $y(t)=-1000(\ r(t)-r(\ t-2\cdot 10^{-3}))$

Where $r(t)$ is the ramp function and i consider $t$ to be the independent variable (time). Wolfram gives me this result. However i'm confused why this is true. Could someone explain to me? Thanks in ...
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How to convert this to an equation?

I need to convert this to an equation so that when a user selects a percentage between 0% and 100% it'll return the correct decimal number based on this scale. As you can see the numbers on the ends ...
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How to represent normal law and a variable intermingled?

Let's consider that a variable y constructed from x $x_i ∈ \left\{1;3;5;7;8\right\}$ $f(x_i)=2x_i+1$ $y_i=f(x_i) + ε_i, ∀i∈ \left\{1;...;5\right\}$ where $ε_i$ is a ...
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Proof that any curve in two dimensions has a modelling differential equation.

I was wondering if anyone knew of a proof stating that any smooth, continuous line drawn in two dimensions must have a differential equation that models it. Best, James.
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Finding selective inverses for functions: how?

So, I have a function $f(x) := \frac{3x}{7+x^2}$ and the question is that the domain is defined such as $x \geq a$, find the minimum value for $a$ for which there exists an inverse of the function. ...
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ACT Strange Math Question “Check my way of solving please”

I got my answer as J. This is my way of solving it. $1 < x + y < 2$ *MINUS $1$ FROM EVERYTHING" \begin{align} x + y - 1 &< 1 \\ +1 &\,+1 \end{align} "PLUS 1 TO EVERYTHING" ...
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Understanding Error Convergence in Numerical Analysis

I'm taking an introductory Numerical Analysis course, and we recently talked about error convergence for iterative algorithms. As a precursor to the question, we denote the absolute error in the ...
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Limitations of Exponential Models

What are the limitations to using an exponential model to explain the rate of cooling of a hot cup of coffee?
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How many steps would it take at least to create a chessboard?

Imagine you have a 8x8 completely white field of squares on your screen. Now you can click on any square. When you do this, all the squares in that column and line (including the one you clicked on ...
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What does it mean to divide a function over another? am I asking for the area in common?

say I have these function in the picture here does f(x)/g(x) in picture A means the red area? and in case the functions didn't cross as in B what does it mean =0 or undefined?
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Labeling of axes in quotient space

It seems to be trivial, but I couldn't find anything. I have a metric space, let us say $\mathbb{R}_{>0}^3$, and a equivalence relation $\sim$, let's say $(x_1,y_1,z_1)\sim(x_2,y_2,z_2)$ if ...
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Identifying the formula for a quartic graphic

I am attempting to help someone with their homework and these concepts are a bit above me. I apologize for the terrible graph drawing. I am using a surface pro 3 and it has an awful camera so I can't ...
36 views

Need help to understand a math task about algebraic and parametric equations

Can anybody please explain this for me?: Find the algebraic and parametric equations of the circle with centre (-2,3) that passes through (1,-1) How do I find the algebraic and parametric ...
58 views

Sketch the complex function: $z\overline{z}+(1+2i)z+(1-2i)+1=0$

Tried sketching the complex function: $z\overline{z}+(1+2i)z+(1-2i)+1=0$ I first simplified it by converting $z=x+yi$ I got: $(x+yi)(x-yi)+(1+2i)(x+yi)+(1-2i)+1=0$ Which gave me this implicit ...
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What's the best open source software for converting plots into Math functions?

I need to complete a year 12 Math homework which involves choosing an object with axial symmetry, plotting its side view on a piece of paper, integrating the resulting curve (assuming a 3D object is ...
108 views

Tool to draw graphs when input points are given

I am writing a dissertation and I have a two collections of data from my research which I would like to compare using graphs. I have the values for abscissa and ordinate and I am looking for some sort ...
64 views

Vector Functions of One Variable

Question A particle moves along the curve of the intersection of the cylinders $y=-x^2$ and $z=x^2$ in the direction in which $x$ increases. (All distances are in cm.) At the instant when the ...
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Geometric interpretation of inverse complex function?

Function $f\colon\mathbb{R}\to\mathbb{R}$ and its inverse $f^{-1}$ are symmetric over line $y=x$. It's easy to imagine inverse of real function, we just have to "flip" the plot over $y=x$. But what ...
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How do I solve this limit

**Find the limit ${x \to 6}$ if $f(f(x))$ ** Any idea how to solve this graphical question on limits?
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Sketching a Graph of a Particle Trajectory

How can I sketch the trajectory of a particle of mass $m$ with a position vector $\mathbf{r} = \cos(\omega t)\,\hat{\mathbf{i}} + \sin(3\omega t)\,\hat{\mathbf{j}}$ ? Will this be a three ...
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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Determine the domain and range of the following relations using set builder notation.

I think I am starting to get the hang of using set builder notation, but I'm getting confused with the end points of these two specific questions. The blue text is hat I have already, but it would ...
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Comparing a function and its estimate

What are some clever ways of comparing (visually) a function with its estimate? For regions where the function does not cross zero, plotting the ratio of the functions and plotting the relative error ...
The function $f(x,y)=\tanh(R-\sqrt{x^2+y^2})$ for a given $R>0$ draws a circle with radius R with maximum and minimum of +1 and -1. This I can see when I plot ...