rm WeaveSupport

quarto/precalc/rational_functions.qmd

@@ -17,21 +17,6 @@ using RealPolynomialRoots
 The `Polynomials` package is "imported" to avoid naming collisions with `SymPy`; names will need to be qualified.
 
 
-```{julia}
-#| echo: false
-#| results: "hidden"
-using CalculusWithJulia.WeaveSupport
-
-const frontmatter = (
-        title = "Rational functions",
-        description = "Calculus with Julia: Rational functions",
-        tags = ["CalculusWithJulia", "precalc", "rational functions"],
-);
-
-using Roots
-
-nothing
-```
 
 ---
 
@@ -427,41 +412,6 @@ The usual recipe for construction follows these steps:
 With the computer, where it is convenient to draw a graph, it might be better to emphasize the sign on the graph of the function. The `sign_chart` function from `CalculusWithJulia` does this by numerically identifying points where the function is $0$ or $\infty$ and indicating the sign as $x$ crosses over these points.
 
 
-```{julia}
-#| echo: false
-# in CalculusWithJuia
-function sign_chart(f, a, b; atol=1e-6)
-    pm(x) = x < 0 ? "-" : x > 0 ? "+" : "0"
-    summarize(f,cp,d) = (∞0=cp, sign_change=pm(f(cp-d)) * " → " * pm(f(cp+d)))
-
-    zs = find_zeros(f, a, b)
-    pts = vcat(a, zs, b)
-    for (u,v) ∈ zip(pts[1:end-1], pts[2:end])
-        zs′ = find_zeros(x -> 1/f(x), u, v)
-        for z′ ∈ zs′
-            flag = false
-            for z ∈ zs
-                if isapprox(z′, z, atol=atol)
-                    flag = true
-                    break
-                end
-            end
-            !flag && push!(zs, z′)
-        end
-    end
-    sort!(zs)
-
-    length(zs) == 0 && return []
-    m,M = extrema(zs)
-    d = min((m-a)/2, (b-M)/2)
-    if length(zs) > 0
-        d′ = minimum(diff(zs))/2
-        d = min(d, d′ )
-    end
-    summarize.(f, zs, d)
-end
-```
-
 ```{julia}
 #| hold: true
 f(x) = x^3 - x
@@ -1046,4 +996,3 @@ L"The $\sin(x)$ oscillates, but the rational function has a horizontal asymptote
 answ = 2
 radioq(choices, answ)
 ```
-