youwen5/site
1
0
Fork 0
mirror of https://github.com/youwen5/site.git synced 2024-11-28 10:53:50 -08:00
Code Issues Projects Releases Packages Wiki Activity Actions

fix: prettierignore in markdown files for certain syntax

Browse source
This commit is contained in:
Youwen Wu 2024-04-24 14:11:58 -07:00
parent eb93966e5f
commit 736018cb9b
Signed by: youwen5
GPG key ID: 865658ED1FE61EC3
1 changed files with 24 additions and 8 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

32
blog/2024/taylor-series/content.md
View file

@ -14,25 +14,35 @@ need a more general method.
We can approximate some non-polynomial functions by constructing a polynomial with the _same We can approximate some non-polynomial functions by constructing a polynomial with the _same
derivatives_ as the function. This is called a _Taylor Polynomial_. 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. > 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 > 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 > 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. > 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 > 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 > 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. > 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 > 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 > 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. > 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 > 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 > 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. > 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. 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: Taylor polynomials take the form:
@ -132,13 +144,17 @@ $$
z \in [c,\,x] z \in [c,\,x]
$$ $$
> [!TIP] This is a fancy way of saying that $z$ is between $c$ and $x$. <!-- prettier-ignore -->
> [!TIP]
> This is a fancy way of saying that $z$ is between $c$ and $x$.
$$ $$
\text{Error} = \left|R_n(x)\right| \text{Error} = \left|R_n(x)\right|
$$ $$
> [!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 $e^x$ #### Applying to $e^x$