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fix: prettierignore in markdown files for certain syntax

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Youwen Wu 2024-04-24 14:11:58 -07:00
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1 changed files with 24 additions and 8 deletions
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32
blog/2024/taylor-series/content.md
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@ -14,25 +14,35 @@ need a more general method.
We can approximate some non-polynomial functions by constructing a polynomial with the _same
derivatives_ as the function. This is called a _Taylor Polynomial_.
> [!NOTE] In general, if $c \neq 0$, it's called a Taylor Polynomial. If $c = 0$, then it's a
<!-- prettier-ignore -->
> [!NOTE]
> In general, if $c \neq 0$, it's called a Taylor Polynomial. If $c = 0$, then it's a
> Maclaurin Polynomial.
> [!CAUTION] test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
<!-- prettier-ignore -->
> [!CAUTION]
> test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
> incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation
> ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in
> voluptate velit esse cillum dolore eu fugiat nulla pariatur.
> [!WARNING] test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
<!-- prettier-ignore -->
> [!WARNING]
> test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
> incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation
> ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in
> voluptate velit esse cillum dolore eu fugiat nulla pariatur.
> [!TIP] test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
<!-- prettier-ignore -->
> [!TIP]
> test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
> incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation
> ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in
> voluptate velit esse cillum dolore eu fugiat nulla pariatur.
> [!IMPORTANT] test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
<!-- prettier-ignore -->
> [!IMPORTANT]
> test lorem ipsum dolor sit amet consectetur adipiscing elit sed do eiusmod tempor
> incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation
> ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in
> voluptate velit esse cillum dolore eu fugiat nulla pariatur.
@ -77,7 +87,9 @@ You can confirm that this polynomial has the same first, second, and third deriv
Taking repeated derivatives like this leads to a common pattern in all Taylor polynomials.
> [!NOTE] We use the notation $P_n(x)$ to denote the $n^{th}$ Taylor polynomial
<!-- prettier-ignore -->
> [!NOTE]
> We use the notation $P_n(x)$ to denote the $n^{th}$ Taylor polynomial
Taylor polynomials take the form:
@ -132,13 +144,17 @@ $$
z \in [c,\,x]
$$
> [!TIP] This is a fancy way of saying that $z$ is between $c$ and $x$.
<!-- prettier-ignore -->
> [!TIP]
> This is a fancy way of saying that $z$ is between $c$ and $x$.
$$
\text{Error} = \left|R_n(x)\right|
$$
> [!NOTE] > $R_n$ would be the "next term" in $P_n(x)$ except we put $z$ instead of $c$.
<!-- prettier-ignore -->
> [!NOTE]
> $R_n$ would be the "next term" in $P_n(x)$ except we put $z$ instead of $c$.
#### Applying to $e^x$