use quarto, not Pluto to render pages

CwJ/derivatives/taylor_series_polynomials.jmd

@@ -14,7 +14,7 @@ using Unitful
 using CalculusWithJulia.WeaveSupport
 using Roots
 
-fig_size = (600, 400)
+fig_size = (800, 600)
 const frontmatter = (
         title = "Taylor Polynomials and other Approximating Polynomials",
         description = "Calculus with Julia: Taylor Polynomials and other Approximating Polynomials",
@@ -564,14 +564,9 @@ output. `SymPy` provides the `removeO` method to strip this. (It is called as `o
 
 
 
-```julia; echo=false
-note("""
+!!! note
+	A Taylor polynomial of degree ``n`` consists of ``n+1`` terms and an error term. The "Taylor series" is an *infinite* collection of terms, the first ``n+1`` matching the Taylor polynomial of degree ``n``. The fact that series are *infinite* means care must be taken when even talking about their existence, unlike a Tyalor polynomial, which is just a polynomial and exists as long as a sufficient number of derivatives are available.
 
-A Taylor polynomial of degree ``n`` consists of ``n+1`` terms and an error term.
-The "Taylor series" is an *infinite* collection of terms, the first ``n+1`` matching the Taylor polynomial of degree ``n``. The fact that series are *infinite* means care must be taken when even talking about their existence, unlike a Tyalor polynomial, which is just a polynomial and exists as long as a sufficient number of derivatives are available.
-
-""")
-```
 
 
 We define a function to compute Taylor polynomials from a function. The following returns a function, not a symbolic object, using `D`, from `CalculusWithJulia`, which is based on `ForwardDiff.derivative`, to find higher-order derivatives:
@@ -965,8 +960,8 @@ choices = [
 "``\\sum_{k=0}^{4} (-1)^k/(2k+1)! \\cdot x^{2k+1}``",
 "``\\sum_{k=0}^{10} x^n/n!``"
 ]
-ans = 3
-radioq(choices, ans)
+answ = 3
+radioq(choices, answ)
 ```
 
 ###### Question
@@ -980,8 +975,8 @@ choices = [
 "``\\sum_{k=0}^{4} (-1)^k/(2k+1)! \\cdot x^{2k+1}``",
 "``\\sum_{k=0}^{10} x^n/n!``"
 ]
-ans = 4
-radioq(choices, ans)
+answ = 4
+radioq(choices, answ)
 ```
 
 
@@ -997,8 +992,8 @@ choices = [
 "``\\sum_{k=0}^{4} (-1)^k/(2k+1)! \\cdot x^{2k+1}``",
 "``\\sum_{k=0}^{10} x^n/n!``"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 ###### Question
@@ -1012,8 +1007,8 @@ choices = [
 "``1/5!``",
 "``2/15``"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 ###### Question
@@ -1028,8 +1023,8 @@ choices = [
 "``x^2``",
 "``x^2 \\cdot (x - x^3/3! + x^5/5!)``"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 
@@ -1048,8 +1043,8 @@ If this is true, then formally evaluating at $x=0$ gives $f(0) = a$, so $a$ is d
 choices = ["``f''''(0) = e``",
 "``f''''(0) = 4 \\cdot 3 \\cdot 2 e = 4! e``",
 "``f''''(0) = 0``"]
-ans = 2
-radioq(choices, ans)
+answ = 2
+radioq(choices, answ)
 ```
 
 ###### Question
@@ -1069,8 +1064,8 @@ yesnoq(true)
 
 ```julia; hold=true; echo=false
 choices =["It is increasing", "It is decreasing", "It both increases and decreases"]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 
@@ -1078,8 +1073,8 @@ radioq(choices, ans)
 
 ```julia; hold=true; echo=false
 choices=["A critical point", "An end point"]
-ans = 2
-radioq(choices, ans)
+answ = 2
+radioq(choices, answ)
 ```
 
 * Which theorem tells you that for a *continuous* function over  *closed* interval, a maximum value will exist?
@@ -1089,8 +1084,8 @@ choices = [
 "The intermediate value theorem",
 "The mean value theorem",
 "The extreme value theorem"]
-ans = 3
-radioq(choices, ans)
+answ = 3
+radioq(choices, answ)
 ```
 
 * What is the *largest* possible value of the error:
@@ -1099,8 +1094,8 @@ radioq(choices, ans)
 choices = [
 "``1/6!\\cdot e^1 \\cdot 1^6``",
 "``1^6 \\cdot 1 \\cdot 1^6``"]
-ans = 1
-radioq(choices,ans)
+answ = 1
+radioq(choices,answ)
 ```
 
 ###### Question
@@ -1115,8 +1110,8 @@ L"The function $e^x$ is increasing, so takes on its largest value at the endpoin
 L"The function has a critical point at $x=1/2$",
 L"The function is monotonic in $k$, so achieves its maximum at $k+1$"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 Assuming the above is right, find the smallest value $k$ guaranteeing a error no more than $10^{-16}$.