fix typos

quarto/precalc/julia_overview.qmd

@@ -626,7 +626,7 @@ xs = range(0, 2pi, length=251)
 ys = [sin(2x) + sin(3x) + sin(4x) for x in xs]
 plot(xs, ys)
 ```
-Plot of $f(x) = \sin(2x) + \sin(3x) + \sin(4x)$ over $[0, 2\pi]$ made by constructing vectors `xs` , `ys` holding $x$ and $y$ coordiinates of points to include
+Plot of $f(x) = \sin(2x) + \sin(3x) + \sin(4x)$ over $[0, 2\pi]$ made by constructing vectors `xs` , `ys` holding $x$ and $y$ coordinates of points to include
 :::
 
 There are different plotting interfaces. Though not shown, all of these `plot` commands produce a plot of `f`, though with minor differences:

quarto/precalc/transformations.qmd

@@ -89,7 +89,7 @@ Starting with two functions and composing them requires nothing more than a soli
 
 ::: {.callout-note}
 ## Infix operator
-Composition of two functions does have an infix operator, `∘`, entered as `\circ[tab]`. This mirrors the mathematical usage of this syntax, though the order of operations are such that calling the composed function on a value requires an extra set of parentheses: `(f∘g)(x)`, as the expresssion `f∘g(x)` evaluates `g(x)` before the composition.
+Composition of two functions does have an infix operator, `∘`, entered as `\circ[tab]`. This mirrors the mathematical usage of this syntax, though the order of operations are such that calling the composed function on a value requires an extra set of parentheses: `(f∘g)(x)`, as the expression `f∘g(x)` evaluates `g(x)` before the composition.
 :::
 
 

quarto/precalc/trig_functions.qmd

@@ -1173,7 +1173,7 @@ The sine function is an *odd* function.
 #| echo: false
 choices = ["odd", "even", "neither"]
 answer = 1
-explanation = "subsitute  `-x` into the exponential formula to see"
+explanation = "substitute  `-x` into the exponential formula to see"
 buttonq(choices, answer; explanation)
 ```
 
@@ -1185,7 +1185,7 @@ buttonq(choices, answer; explanation)
 #| echo: false
 choices = ["odd", "even", "neither"]
 answer = 2
-explanation = L"The value of $\cosh(-x)$ is the $y$ position of the point $(x,y)$ refelected through the $y$ axis, so is unchanged."
+explanation = L"The value of $\cosh(-x)$ is the $y$ position of the point $(x,y)$ reflected through the $y$ axis, so is unchanged."
 buttonq(choices, answer; explanation)
 ```