daviddoji/CalculusWithJuliaNotes.jl
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use quarto, not Pluto to render pages

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jverzani
2022-07-24 16:38:24 -04:00
parent 93c993206a
commit 7b37ca828c
879 changed files with 793311 additions and 2678 deletions
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CwJ/limits/continuity.jmd
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@@ -86,12 +86,10 @@ continuity and *left* continuity at a point, where the limit in the
defintion is replaced by a right or left limit, as appropriate.
```julia; echo=false
alert("""
The limit in the definition of continuity is the basic limit and not an extended sense where
infinities are accounted for.
""")
```
!!! warning
The limit in the definition of continuity is the basic limit and not an extended sense where
infinities are accounted for.
##### Examples of continuity
Most familiar functions are continuous everywhere.
@@ -256,8 +254,8 @@ f+g,~ f-g,~ f\cdot g,~ f\circ g,~ f/g
```julia; hold=true; echo=false
choices = ["``f+g``", "``f-g``", "``f\\cdot g``", "``f\\circ g``", "``f/g``"]
ans = length(choices)
radioq(choices, ans)
answ = length(choices)
radioq(choices, answ)
```
###### Question
@@ -268,16 +266,16 @@ When will $f\circ g$ be continuous?
```julia; hold=true; echo=false
choices = [L"For all $x$", L"For all $x > 0$", L"For all $x$ where $\sin(x) > 0$"]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
When will $g \circ f$ be continuous?
```julia; hold=true; echo=false
choices = [L"For all $x$", L"For all $x > 0$", L"For all $x$ where $\sin(x) > 0$"]
ans = 3
radioq(choices, ans, keep_order=true)
answ = 3
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -290,8 +288,8 @@ L"The function $g$ is continuous everywhere",
L"The function $f$ is continuous everywhere",
L"The function $g$ is continuous everywhere and $f$ is continuous on the range of $g$",
L"The function $f$ is continuous everywhere and $g$ is continuous on the range of $f$"]
ans = 3
radioq(choices, ans, keep_order=true)
answ = 3
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -304,8 +302,8 @@ L"When $x > 2$",
L"When $x \geq 2$",
L"When $x \leq 2$",
L"For $x \geq 0$"]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
@@ -375,8 +373,8 @@ Suppose $f(x)$, $g(x)$, and $h(x)$ are continuous functions on $(a,b)$. If $a <
choices = [L"No, as $g(c)$ may not be in the interval $(a,b)$",
"Yes, composition of continuous functions results in a continuous function, so the limit is just the function value."
]
ans=1
radioq(choices, ans)
answ=1
radioq(choices, answ)
```
###### Question
@@ -446,6 +444,6 @@ choices = ["Can't tell",
"``-1.0``",
"``0.0``"
]
ans = 1
radioq(choices, ans)
answ = 1
radioq(choices, answ)
```