diff --git a/ptx/review-exercises-limits.ptx b/ptx/review-exercises-limits.ptx
index 8c14ddf4f..09dd87313 100644
--- a/ptx/review-exercises-limits.ptx
+++ b/ptx/review-exercises-limits.ptx
@@ -272,7 +272,7 @@
For a numerical approximation, make a table:
-
+ x
diff --git a/ptx/sec_Graphical_Numerical.ptx b/ptx/sec_Graphical_Numerical.ptx
index 31477d448..700a4a06b 100644
--- a/ptx/sec_Graphical_Numerical.ptx
+++ b/ptx/sec_Graphical_Numerical.ptx
@@ -1072,7 +1072,7 @@
Slope field for the logistic differential equation \yp = y(1-y) from
- Graph of slope field for the logistic differential equation y’=y(1-y) from the example.
+ Graph of slope field for the logistic differential equation y'=y(1-y) from the example.
@@ -1160,7 +1160,7 @@
with a few representative solution curves
- Graph of slope field for the logistic differential equation y’=y(1-y) with representative solution curves.
+ Graph of slope field for the logistic differential equation y'=y(1-y) with representative solution curves.
Finding the extreme values of f(x)= 2x^3+3x^2-12x in
-
+ xf(x)
@@ -879,7 +879,7 @@
Finding the extreme values of a piecewise-defined function in
-
+ xf(x)
@@ -983,7 +983,7 @@
Finding the extrema of f(x)= \cos\mathopen{}\left(x^2\right)\mathclose{} in
-
+ xf(x)
@@ -1094,7 +1094,7 @@
Finding the extrema of the half-circle in
-
+ xf(x)
diff --git a/ptx/sec_hyperbolic.ptx b/ptx/sec_hyperbolic.ptx
index e6c1ef962..cfd78f0ff 100644
--- a/ptx/sec_hyperbolic.ptx
+++ b/ptx/sec_hyperbolic.ptx
@@ -781,7 +781,7 @@
Domains and ranges of the hyperbolic and inverse hyperbolic functions
-
+ FunctionDomainRange
diff --git a/ptx/sec_limit_continuity.ptx b/ptx/sec_limit_continuity.ptx
index 612bf9227..33ad59c5d 100644
--- a/ptx/sec_limit_continuity.ptx
+++ b/ptx/sec_limit_continuity.ptx
@@ -1425,7 +1425,7 @@
Iterations of the Bisection Method of Root Finding
-
+ Iteration #IntervalMidpoint Sign
@@ -3274,7 +3274,7 @@
If f(m)\gt 0 at the midpoint m, put + for the midpoint sign. If f(m)\lt 0, put - for the midpoint sign.
-
+ IterationIntervalMidpoint Sign
@@ -3364,7 +3364,7 @@
If f(m)\gt 0 at the midpoint m, put + for the midpoint sign. If f(m)\lt 0, put - for the midpoint sign.
-
+ IterationIntervalMidpoint Sign
@@ -3454,7 +3454,7 @@
If f(m)\gt 0 at the midpoint m, put + for the midpoint sign. If f(m)\lt 0, put - for the midpoint sign.
-
+ IterationIntervalMidpoint Sign
@@ -3544,7 +3544,7 @@
If f(m)\gt 0 at the midpoint m, put + for the midpoint sign. If f(m)\lt 0, put - for the midpoint sign.
-
+ IterationIntervalMidpoint Sign
diff --git a/ptx/sec_limit_infty.ptx b/ptx/sec_limit_infty.ptx
index 55dc94d27..6fb8b198b 100644
--- a/ptx/sec_limit_infty.ptx
+++ b/ptx/sec_limit_infty.ptx
@@ -759,7 +759,7 @@
Observing that f(x)=\sin(1/x) has no limit as x\to0 in
-
+ x\sin(1/x)
@@ -1434,7 +1434,7 @@
The difference quotient evaluated at values of h near 0
-
+ h\frac{f(1+h)-f(1)}{h}
@@ -1994,7 +1994,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2087,7 +2087,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2183,7 +2183,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2294,7 +2294,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2405,7 +2405,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2512,7 +2512,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2619,7 +2619,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2724,7 +2724,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2829,7 +2829,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -2937,7 +2937,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -3028,7 +3028,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -3117,7 +3117,7 @@
For a numerical approximation, make a table:
-
+ x
@@ -3218,7 +3218,7 @@
For a numerical approximation, make a table:
-
+ x\big\lfloor\lvert x\rvert\big\rfloor !
@@ -3333,7 +3333,7 @@
For a numerical approximation, make a table:
-
+ x\big\lfloor\lvert x\rvert\big\rfloor !
@@ -3482,7 +3482,7 @@
All quantities are functions of time, t (min), defined as follows:
-
+ V(t)Volume of water in a tank (\text{m}^3) at time, t
diff --git a/ptx/sec_shell_method.ptx b/ptx/sec_shell_method.ptx
index 2185229f5..d7df5a394 100644
--- a/ptx/sec_shell_method.ptx
+++ b/ptx/sec_shell_method.ptx
@@ -1447,7 +1447,7 @@
-
+ ta_\text{T}a_\text{N}
diff --git a/ptx/sec_taylor_series.ptx b/ptx/sec_taylor_series.ptx
index c831d5e4d..32c31a839 100644
--- a/ptx/sec_taylor_series.ptx
+++ b/ptx/sec_taylor_series.ptx
@@ -616,7 +616,7 @@
Important Taylor Series Expansions
-
+ Function and SeriesFirst Few TermsInterval of
diff --git a/ptx/sec_vector_intro.ptx b/ptx/sec_vector_intro.ptx
index 86ca0533b..4c029bcea 100644
--- a/ptx/sec_vector_intro.ptx
+++ b/ptx/sec_vector_intro.ptx
@@ -291,7 +291,7 @@
The x and y axes are drawn from -4 to 4. Two vectors are drawn.
- The vector PP’ is in the first quadrant it is downward facing, it starts from
+ The vector PP' is in the first quadrant it is downward facing, it starts from
P=(3, 2) and ends at P'=(5, 1). The second vector RS from (-3, -2)
to (-1, 2). This vector lies midway between the second and the third quadrant.