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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58
CwJ/derivatives/derivatives.jmd
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@@ -19,7 +19,7 @@ const frontmatter = (
tags = ["CalculusWithJulia", "derivatives", "derivatives"],
);
fig_size=(600, 400)
fig_size=(800, 600)
nothing
```
@@ -1199,16 +1199,16 @@ At which of these points $c= 1/2, 1, 3/2$ is the derivative negative?
```julia; hold=true; echo=false
choices = ["``1/2``", "``1``", "``3/2``"]
ans = 1
radioq(choices, ans, keep_order=true)
answ = 1
radioq(choices, answ, keep_order=true)
```
Which value looks bigger from reading the graph:
```julia; hold=true; echo=false
choices = ["``f(1)``", "``f(3/2)``"]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
At $0.708 \dots$ and $1.65\dots$ the derivative has a common value. What is it?
@@ -1229,8 +1229,8 @@ At $x = -2.5$ the derivative is postive or negative?
```julia; hold=true; echo=false
choices = ["positive", "negative"]
ans = 1
radioq(choices, ans, keep_order=true)
answ = 1
radioq(choices, answ, keep_order=true)
```
@@ -1238,16 +1238,16 @@ At $x=0$ the derivative is postive or negative?
```julia; hold=true; echo=false
choices = ["positive", "negative"]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
At $x = 2.5$ the derivative is postive or negative?
```julia; hold=true; echo=false
choices = ["positive", "negative"]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -1256,8 +1256,8 @@ Compute the derivative of $e^x$ using `limit`. What do you get?
```julia; hold=true; echo=false
choices = ["``e^x``", "``x^e``", "``(e-1)x^e``", "``e x^{(e-1)}``", "something else"]
ans = 1
radioq(choices, ans, keep_order=true)
answ = 1
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -1266,8 +1266,8 @@ Compute the derivative of $x^e$ using `limit`. What do you get?
```julia; hold=true; echo=false
choices = ["``e^x``", "``x^e``", "``(e-1)x^e``", "``e x^{(e-1)}``", "something else"]
ans = 5
radioq(choices, ans, keep_order=true)
answ = 5
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -1276,8 +1276,8 @@ Compute the derivative of $e^{e\cdot x}$ using `limit`. What do you get?
```julia; hold=true; echo=false
choices = ["``e^x``", "``x^e``", "``(e-1)x^e``", "``e x^{(e-1)}``", "``e \\cdot e^{e\\cdot x}``", "something else"]
ans = 5
radioq(choices, ans, keep_order=true)
answ = 5
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -1295,8 +1295,8 @@ choices = [
L" $1$, as this is clearly the analog of the limit of $\sin(h)/h$.",
L"Does not exist. The answer is $0/0$ which is undefined",
L" $0$, as this expression is the derivative of cosine at $0$. The answer follows, as cosine clearly has a tangent line with slope $0$ at $x=0$."]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
###### Question
@@ -1310,8 +1310,8 @@ choices = [
"``f'(x) = f(x)``",
"``f'(x) = -f(x)``"
]
ans= 1
radioq(choices, ans)
answ= 1
radioq(choices, answ)
```
@@ -1326,8 +1326,8 @@ choices = [
"``f''(x) = -g(x)``",
"``f''(x) = f(x)``",
"``f''(x) = -f(x)``"]
ans= 3
radioq(choices, ans)
answ= 3
radioq(choices, answ)
```
@@ -1381,8 +1381,8 @@ L"If the graphs of $f$ and $g$ are translations up and down, the tangent line at
L"If the graphs of $f$ and $g$ are rescalings of each other through $g(x)=f(x/c)$, $c > 1$. Then the tangent line for corresponding points is the same.",
L"If the graphs of $f$ and $g$ are rescalings of each other through $g(x)=cf(x)$, $c > 1$. Then the tangent line for corresponding points is the same."
]
ans = 1
radioq(choices, ans)
answ = 1
radioq(choices, answ)
```
@@ -1409,8 +1409,8 @@ choices = [
"``f'(x) = -k^2 \\cdot f(x)``",
"``f''(x) = k^2 \\cdot f(x)``",
"``f''(x) = -k^2 \\cdot f(x)``"]
ans = 4
radioq(choices, ans)
answ = 4
radioq(choices, answ)
```
###### Question
@@ -1424,8 +1424,8 @@ choices = [
"``f'(x) = -k^2 \\cdot f(x)``",
"``f''(x) = k^2 \\cdot f(x)``",
"``f''(x) = -k^2 \\cdot f(x)``"]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
##### Question