typos

quarto/limits/continuity.qmd

@@ -73,7 +73,7 @@ This speaks to continuity at a point, we can extend this to continuity over an i
 
 
 
-Finally, as with limits, it can be convenient to speak of *right* continuity and *left* continuity at a point, where the limit in the defintion is replaced by a right or left limit, as appropriate.
+Finally, as with limits, it can be convenient to speak of *right* continuity and *left* continuity at a point, where the limit in the definition is replaced by a right or left limit, as appropriate.
 
 
 :::{.callout-warning}

quarto/limits/intermediate_value_theorem.qmd

@@ -86,7 +86,7 @@ Suppose we have a continuous function $f(x)$ on $[a,b]$ with $f(a) < 0$ and $f(b
 We use this fact when building a "sign chart" of a polynomial function. Between any two consecutive real zeros the polynomial can not change sign. (Why?) So a "test point" can be used to determine the sign of the function over an entire interval.
 
 
-Here, we use the Bolzano theorem to give an algorithm - the *bisection method* - to locate the value $c$ under the assumption $f$ is continous on $[a,b]$ and changes sign between $a$ and $b$.
+Here, we use the Bolzano theorem to give an algorithm - the *bisection method* - to locate the value $c$ under the assumption $f$ is continuous on $[a,b]$ and changes sign between $a$ and $b$.
 
 
 ```{julia}
@@ -603,7 +603,7 @@ The output of `find_zeros` is a vector of values. To check that each value is an
 f₁.(zs)
 ```
 
-(For a continuous function this should be the case that the values returned by `find_zeros` are approximate zeros. Bear in mind that if $f$ is not continous the algorithm might find jumping points that are not zeros and may not even be in the domain of the function.)
+(For a continuous function this should be the case that the values returned by `find_zeros` are approximate zeros. Bear in mind that if $f$ is not continuous the algorithm might find jumping points that are not zeros and may not even be in the domain of the function.)
 
 
 ### An alternate interface to `find_zero`

quarto/limits/limits.qmd

@@ -235,7 +235,7 @@ annotate!([(0,0+Δ,"A"), (x-Δ,y+Δ/4, "B"), (1+Δ/2,y/x, "C"),
 annotate!([(.2*cos(θ/2), 0.2*sin(θ/2), "θ")])
 imgfile = tempname() * ".png"
 savefig(p, imgfile)
-caption = "Triangle  ABD has less area than the shaded wedge, which has less area than triangle ACD. Their respective areas are ``(1/2)\\sin(\\theta)``, ``(1/2)\\theta``, and ``(1/2)\\tan(\\theta)``. The inequality used to show ``\\sin(x)/x`` is bounded below by ``\\cos(x)`` and above by ``1`` comes from a division by ``(1/2) \\sin(x)`` and taking reciprocals.
+caption = "Triangle ``ABD` has less area than the shaded wedge, which has less area than triangle ``ACD``. Their respective areas are ``(1/2)\\sin(\\theta)``, ``(1/2)\\theta``, and ``(1/2)\\tan(\\theta)``. The inequality used to show ``\\sin(x)/x`` is bounded below by ``\\cos(x)`` and above by ``1`` comes from a division by ``(1/2) \\sin(x)`` and taking reciprocals.
 "
 ImageFile(imgfile, caption)
 ```
@@ -1666,7 +1666,7 @@ Should `SymPy` have needed an assumption like
 
 
 ```{julia}
-@syms a::postive
+@syms a::positive
 ```
 
 ```{julia}

quarto/limits/limits_extensions.qmd

@@ -103,7 +103,7 @@ Let's loosen up the language in the definition of a limit to read:
 The $\epsilon-\delta$ definition has $V = (L-\epsilon, L + \epsilon)$ and $U=(c-\delta, c+\delta)$. This is a rewriting of $L-\epsilon < f(x) < L + \epsilon$ as $|f(x) - L| < \epsilon$.
 
 
-Now for the defintion:
+Now for the definition:
 
 
 > A function $f(x)$ has a limit on the right of $c$, written $\lim_{x  \rightarrow c+}f(x) = L$ if for every $\epsilon > 0$, there exists a  $\delta > 0$ such that whenever $0 < x - c < \delta$ it holds that  $|f(x) - L| < \epsilon$. That is, $U$ is $(c, c+\delta)$
@@ -573,7 +573,7 @@ fx, gx = exp(x^2), exp(x)^2
 limit(gx^n / fx, x => oo)
 ```
 
-A negative test for compatability is the following: if
+A negative test for compatibility is the following: if
 
 
 $$