daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2024-05-22 07:55:20 -04:00
parent f710cded15
commit 771bb06aa3
50 changed files with 120 additions and 426 deletions
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quarto/derivatives/taylor_series_polynomials.qmd
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@@ -64,7 +64,7 @@ gif(anim, imgfile, fps = 1)
caption = L"""
Illustration of the Taylor polynomial of degree $k$, $T_k(x)$, at $c=0$ and its graph overlayed on that of the function $1 - \cos(x)$.
Illustration of the Taylor polynomial of degree $k$, $T_k(x)$, at $c=0$ and its graph overlaid on that of the function $1 - \cos(x)$.
"""
@@ -921,7 +921,7 @@ end
gᵏs
```
We can see the expected `g' = 1/f'` (where the point of evalution is $g'(y) = 1/f'(f^{-1}(y))$ is not written). In addition, we get 3 more formulas, hinting that the answers grow rapidly in terms of their complexity.
We can see the expected `g' = 1/f'` (where the point of evaluation is $g'(y) = 1/f'(f^{-1}(y))$ is not written). In addition, we get 3 more formulas, hinting that the answers grow rapidly in terms of their complexity.
In the above, for each `n`, the code above sets up the two sides, `left` and `right`, of an equation involving the higher-order derivatives of $g$. For example, when `n=2` we have: