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jverzani
2022-07-25 20:51:08 -04:00
parent bce4ce7fa0
commit 6712bb02c4
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28
quarto/limits/continuity.qmd
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@@ -1,33 +1,7 @@
# Continuity
```{julia}
#| echo: false
import Logging
Logging.disable_logging(Logging.Info) # or e.g. Logging.Info
Logging.disable_logging(Logging.Warn)
import SymPy
function Base.show(io::IO, ::MIME"text/html", x::T) where {T <: SymPy.SymbolicObject}
println(io, "<span class=\"math-left-align\" style=\"padding-left: 4px; width:0; float:left;\"> ")
println(io, "\\[")
println(io, sympy.latex(x))
println(io, "\\]")
println(io, "</span>")
end
# hack to work around issue
import Markdown
import CalculusWithJulia
function CalculusWithJulia.WeaveSupport.ImageFile(d::Symbol, f::AbstractString, caption; kwargs...)
nm = joinpath("..", string(d), f)
u = "![$caption]($nm)"
Markdown.parse(u)
end
nothing
```
{{< include ../_common_code.qmd >}}
This section uses these add-on packages:

28
quarto/limits/intermediate_value_theorem.qmd
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@@ -1,33 +1,7 @@
# Implications of continuity
```{julia}
#| echo: false
import Logging
Logging.disable_logging(Logging.Info) # or e.g. Logging.Info
Logging.disable_logging(Logging.Warn)
import SymPy
function Base.show(io::IO, ::MIME"text/html", x::T) where {T <: SymPy.SymbolicObject}
println(io, "<span class=\"math-left-align\" style=\"padding-left: 4px; width:0; float:left;\"> ")
println(io, "\\[")
println(io, sympy.latex(x))
println(io, "\\]")
println(io, "</span>")
end
# hack to work around issue
import Markdown
import CalculusWithJulia
function CalculusWithJulia.WeaveSupport.ImageFile(d::Symbol, f::AbstractString, caption; kwargs...)
nm = joinpath("..", string(d), f)
u = "![$caption]($nm)"
Markdown.parse(u)
end
nothing
```
{{< include ../_common_code.qmd >}}
This section uses these add-on packages:

65
quarto/limits/limits.qmd
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@@ -1,33 +1,7 @@
# Limits
```{julia}
#| echo: false
import Logging
Logging.disable_logging(Logging.Info) # or e.g. Logging.Info
Logging.disable_logging(Logging.Warn)
import SymPy
function Base.show(io::IO, ::MIME"text/html", x::T) where {T <: SymPy.SymbolicObject}
println(io, "<span class=\"math-left-align\" style=\"padding-left: 4px; width:0; float:left;\"> ")
println(io, "\\[")
println(io, sympy.latex(x))
println(io, "\\]")
println(io, "</span>")
end
# hack to work around issue
import Markdown
import CalculusWithJulia
function CalculusWithJulia.WeaveSupport.ImageFile(d::Symbol, f::AbstractString, caption; kwargs...)
nm = joinpath("..", string(d), f)
u = "![$caption]($nm)"
Markdown.parse(u)
end
nothing
```
{{< include ../_common_code.qmd >}}
This section uses the following add-on packages:
@@ -407,6 +381,43 @@ The graphical approach to limits - plotting $f(x)$ around $c$ and observing if t
##### Example
This example illustrates the same limit a different way. Sliding the $x$ value towards $0$ shows $f(x) = \sin(x)/x$ approaches a value of $1$.
```{=html}
<div id="jsxgraph" style="width: 500px; height: 500px;"></div>
```
```{ojs}
//| echo: false
//| output: false
JXG = require("jsxgraph")
b = JXG.JSXGraph.initBoard('jsxgraph', {
boundingbox: [-6, 1.2, 6,-1.2], axis:true
});
f = function(x) {return Math.sin(x) / x;};
graph = b.create("functiongraph", [f, -6, 6])
seg = b.create("line", [[-6,0], [6,0]], {fixed:true});
X = b.create("glider", [2, 0, seg], {name:"x", size:4});
P = b.create("point", [function() {return X.X()}, function() {return f(X.X())}], {name:""});
Q = b.create("point", [0, function() {return P.Y();}], {name:"f(x)"});
segup = b.create("segment", [P,X], {dash:2});
segover = b.create("segment", [P, [0, function() {return P.Y()}]], {dash:2});
txt = b.create('text', [2, 1, function() {
return "x = " + X.X().toFixed(4) + ", f(x) = " + P.Y().toFixed(4);
}]);
```
##### Example
Consider now the following limit

28
quarto/limits/limits_extensions.qmd
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@@ -1,33 +1,7 @@
# Limits, issues, extensions of the concept
```{julia}
#| echo: false
import Logging
Logging.disable_logging(Logging.Info) # or e.g. Logging.Info
Logging.disable_logging(Logging.Warn)
import SymPy
function Base.show(io::IO, ::MIME"text/html", x::T) where {T <: SymPy.SymbolicObject}
println(io, "<span class=\"math-left-align\" style=\"padding-left: 4px; width:0; float:left;\"> ")
println(io, "\\[")
println(io, sympy.latex(x))
println(io, "\\]")
println(io, "</span>")
end
# hack to work around issue
import Markdown
import CalculusWithJulia
function CalculusWithJulia.WeaveSupport.ImageFile(d::Symbol, f::AbstractString, caption; kwargs...)
nm = joinpath("..", string(d), f)
u = "![$caption]($nm)"
Markdown.parse(u)
end
nothing
```
{{< include ../_common_code.qmd >}}
This section uses the following add-on packages:

26
quarto/limits/process.jl
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@@ -1,26 +0,0 @@
using CwJWeaveTpl
fnames = [
"limits",
"limits_extensions",
#
"continuity",
"intermediate_value_theorem"
]
process_file(nm; cache=:off) = CwJWeaveTpl.mmd(nm * ".jmd", cache=cache)
function process_files(;cache=:user)
for f in fnames
@show f
process_file(f, cache=cache)
end
end
"""
## TODO limits
"""