daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2024-05-22 07:55:20 -04:00
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quarto/precalc/plotting.qmd
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@@ -352,7 +352,7 @@ plot(0:pi/4:2pi, sin)
#### NaN values
At times it is not desirable to draw lines between each succesive point. For example, if there is a discontinuity in the function or if there were a vertical asymptote, such as what happens at $0$ with $f(x) = 1/x$.
At times it is not desirable to draw lines between each successive point. For example, if there is a discontinuity in the function or if there were a vertical asymptote, such as what happens at $0$ with $f(x) = 1/x$.
The most straightforward plot is dominated by the vertical asymptote at $x=0$:
@@ -667,7 +667,7 @@ Playing with the toy makes a few things become clear:
These all apply to parametric plots, as the Etch A Sketch trace is no more than a plot of $(f(t), g(t))$ over some range of values for $t$, where $f$ describes the movement in time of the left knob and $g$ the movement in time of the right.
Now, we revist the last problem in the context of this. We saw in the last problem that the parametric graph was nearly a line - so close the eye can't really tell otherwise. That means that the growth in both $f(t) = t^3$ and $g(t)=t - \sin(t)$ for $t$ around $0$ are in a nearly fixed ratio, as otherwise the graph would have more curve in it.
Now, we revisit the last problem in the context of this. We saw in the last problem that the parametric graph was nearly a line - so close the eye can't really tell otherwise. That means that the growth in both $f(t) = t^3$ and $g(t)=t - \sin(t)$ for $t$ around $0$ are in a nearly fixed ratio, as otherwise the graph would have more curve in it.
##### Example: Spirograph