use quarto, not Pluto to render pages

CwJ/limits/limits.jmd

@@ -17,7 +17,7 @@ const frontmatter = (
         description = "Calculus with Julia: Limits",
         tags = ["CalculusWithJulia", "limits", "limits"],
 );
-const fig_size=(400, 300)
+fig_size=(800, 600)
 nothing
 ```
 
@@ -287,8 +287,9 @@ This progression can be seen to be increasing. Cauchy, in his treatise, can see
 ```math
 \begin{align*}
 (1 + \frac{1}{m})^n &= 1 + \frac{1}{1} + \frac{1}{1\cdot 2}(1 = \frac{1}{m}) +  \\
-& \frac{1}{1\cdot 2\cdot 3}(1 - \frac{1}{m})(1 -  \frac{2}{m}) + \cdots +
-& \frac{1}{1 \cdot 2 \cdot \cdots \cdot m}(1 - \frac{1}{m}) \cdot \cdots \cdot (1 - \frac{m-1}{m}).
+& \frac{1}{1\cdot 2\cdot 3}(1 - \frac{1}{m})(1 -  \frac{2}{m}) + \cdots \\
+&+
+\frac{1}{1 \cdot 2 \cdot \cdots \cdot m}(1 - \frac{1}{m}) \cdot \cdots \cdot (1 - \frac{m-1}{m}).
 \end{align*}
 ```
 
@@ -1088,8 +1089,8 @@ plot(f, 0,2)
 
 
 ```julia; hold=true; echo=false
-ans = 1/4
-numericq(ans, 1e-1)
+answ = 1/4
+numericq(answ, 1e-1)
 ```
 
 
@@ -1158,36 +1159,38 @@ numericq(val, 1e-2)
 Select the graph for which there is no limit at ``a``.
 
 ```julia; hold=true; echo=false
-p1 = plot(;axis=nothing, legend=false)
-title!(p1, "(a)")
-plot!(p1, x -> x^2, 0, 2, color=:black)
-plot!(p1, zero, linestyle=:dash)
-annotate!(p1,[(1,0,"a")])
+let
+    p1 = plot(;axis=nothing, legend=false)
+    title!(p1, "(a)")
+    plot!(p1, x -> x^2, 0, 2, color=:black)
+    plot!(p1, zero, linestyle=:dash)
+    annotate!(p1,[(1,0,"a")])
 
-p2 = plot(;axis=nothing, legend=false)
-title!(p2, "(b)")
-plot!(p2, x -> 1/(1-x), 0, .95, color=:black)
-plot!(p2, x-> -1/(1-x), 1.05, 2, color=:black)
-plot!(p2, zero, linestyle=:dash)
-annotate!(p2,[(1,0,"a")])
+    p2 = plot(;axis=nothing, legend=false)
+    title!(p2, "(b)")
+    plot!(p2, x -> 1/(1-x), 0, .95, color=:black)
+    plot!(p2, x-> -1/(1-x), 1.05, 2, color=:black)
+    plot!(p2, zero, linestyle=:dash)
+    annotate!(p2,[(1,0,"a")])
 
-p3 = plot(;axis=nothing, legend=false)
-title!(p3, "(c)")
-plot!(p3, sinpi, 0, 2, color=:black)
-plot!(p3, zero, linestyle=:dash)
-annotate!(p3,[(1,0,"a")])
+    p3 = plot(;axis=nothing, legend=false)
+    title!(p3, "(c)")
+    plot!(p3, sinpi, 0, 2, color=:black)
+    plot!(p3, zero, linestyle=:dash)
+    annotate!(p3,[(1,0,"a")])
 
-p4 = plot(;axis=nothing, legend=false)
-title!(p4, "(d)")
-plot!(p4, x -> x^x, 0, 2, color=:black)
-plot!(p4, zero, linestyle=:dash)
-annotate!(p4,[(1,0,"a")])
+    p4 = plot(;axis=nothing, legend=false)
+    title!(p4, "(d)")
+    plot!(p4, x -> x^x, 0, 2, color=:black)
+    plot!(p4, zero, linestyle=:dash)
+    annotate!(p4,[(1,0,"a")])
 
-l = @layout[a b; c d]
-p = plot(p1, p2, p3, p4, layout=l)
-imgfile = tempname() * ".png"
-savefig(p, imgfile)
-hotspotq(imgfile, (1/2,1), (1/2,1))
+    l = @layout[a b; c d]
+    p = plot(p1, p2, p3, p4, layout=l)
+    imgfile = tempname() * ".png"
+    savefig(p, imgfile)
+    hotspotq(imgfile, (1/2,1), (1/2,1))
+end
 ```
 
 ###### Question
@@ -1209,8 +1212,8 @@ What is $L$?
 
 ```julia; hold=true; echo=false
 choices = ["``0``", "``1``", "``e^x``"]
-ans = 3
-radioq(choices, ans)
+answ = 3
+radioq(choices, answ)
 ```
 
 
@@ -1237,8 +1240,8 @@ Using the last result, what is the value of $L$?
 
 ```julia; hold=true; echo=false
 choices = ["``\\cos(x)``", "``\\sin(x)``", "``1``", "``0``", "``\\sin(h)/h``"]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 
@@ -1309,8 +1312,8 @@ the fact that $x$ is measured in radians. Try to find this limit:
 
 ```julia; hold=true; echo=false
 choices = [q"0", q"1", q"pi/180", q"180/pi"]
-ans = 3
-radioq(choices, ans)
+answ = 3
+radioq(choices, answ)
 ```
 
 
@@ -1318,8 +1321,8 @@ What is the limit `limit(sinpi(x)/x, x => 0)`?
 
 ```julia; hold=true; echo=false
 choices = [q"0", q"1", q"pi", q"1/pi"]
-ans = 3
-radioq(choices, ans)
+answ = 3
+radioq(choices, answ)
 ```
 
 ###### Question: limit properties
@@ -1388,8 +1391,8 @@ choices = [
 "Yes, the value is `-11.5123`",
 "No, the value heads to negative infinity"
 ];
-ans = 3;
-radioq(choices, ans)
+answ = 3;
+radioq(choices, answ)
 ```
 
 ###### Question
@@ -1433,8 +1436,8 @@ What is `limit(ex, x => 0)`?
 
 ```julia; hold=true; echo=false
 choices = ["``e^{km}``", "``e^{k/m}``", "``k/m``", "``m/k``", "``0``"]
-answer = 1
-radioq(choices, answer)
+answwer = 1
+radioq(choices, answwer)
 ```
 
 ###### Question
@@ -1511,8 +1514,8 @@ between both $g$ and $h$, so must to have a limit of $0$.
 """,
 	L"The functions $g$ and $h$ squeeze each other as $g(x) > h(x)$",
          L"The function $f$ has no limit - it oscillates too much near $0$"]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 (The [Wikipedia](https://en.wikipedia.org/wiki/Squeeze_theorem) entry for the squeeze theorem has this unverified, but colorful detail: