AC Multivariable Errata

Below are known typographical errors or mistakes found
in the July 27, 2015 version of Active Calculus – Multivariable. These errors
have been corrected in the newest version, dated January 2, 2106. We appreciate
the opportunity to correct all errors for future releases, so please send us
corrections if you see them.

Thanks

· Page
39. In part (b) of Exercise 2 the sides should be called **a** and **b**.

·
Page 62. The missing Figure
reference is to Figure 9.54. (Reported by Jon Barker
and class, St. Ignatius High School, Cleveland, OH.)

·
Page 64, Exercise 2. The
vertical axis should have length 2*b*.
(Reported by Jon Barker and class, St.
Ignatius High School, Cleveland, OH.)

·
Page 65, Exercise 4. There is
only one point of intersection of the lines, so the word “points” should be
replaced with “point”. (Reported by Jon Barker and
class, St. Ignatius High School, Cleveland, OH.)

·
Page 67, Activity 9.26 (a). Since the
vector **r**(*t*+*h*) – **r**(*t*) is already in Figure 9.55, the
directions should be to identify the object instead of sketching it. (Reported
by Jon Barker and class, St. Ignatius High
School, Cleveland, OH.)

·
Page 68, Activity 9.26 (b). Since a value
of *h* is not supplied, the directions
should be to sketch a representative vector with *h* < 1. (Reported by Jon Barker and
class, St. Ignatius High School, Cleveland, OH.)

·
Page 70, part 3 of the theorem, derivative
of the dot product. The last summand should be **r**(*t*) ∙ **s**′(*t*). (Reported by Brian W. Gleason, Nevada State
College.)

·
Page 70. The right hand side of Activity
9.28, part g, has the **a**
and **v** in the wrong places. (Reported
by Brian W. Gleason, Nevada State
College, found by his students.)

·
Page 76, Exercise 2. As written, the two
curves do not intersect. Changing the existing curves so that the z component
of **r** is 1/*t* and the *z* component of **w** is sin(π*s*/4) causes the curves to intersect at
(2,0,1). In future editions the curves
will be changed to **r**(*t*) = 〈*t *+ 1, cos(π*t*/2), 1/(1+*t*)〉 and **w**(*s*) = 〈*s*^{2},
sin(π*s*/2), *s*〉.
(Reported by Jon Barker and class, St.
Ignatius High School, Cleveland, OH.)

·
Page 76, Exercise 3. The point (3,4,5) is not on the surface. The function *f* should be defined as *f*(*x*,*y*) = (*x*^{2}
+ *y*^{2})^{1/2}.
(Reported by Jon Barker and class, St.
Ignatius High School, Cleveland, OH.)

·
Page 89, Exercise 2 of Section 9.8. The
function given in part (d) should be the same as that one in part (a).
(Reported by Brian W.
Gleason, Nevada State College.)

·
Page 90, Exercise 3. There is a **k** missing in the definition of **r**. (Reported by Jon Barker and class, St. Ignatius High School, Cleveland, OH.)

·
Page 90, Exercise 3 (c). The denominator
of the formula for **N**(*t*) should be |**T**'(*t*)|.
(Reported by Jon Barker, St. Ignatius High
School, Cleveland, OH.)

· Page
92. The caption to Figure 10.1 gives the wrong function for the graph – it
should be

*f*(*x*) = 3-*x*.
(Reported by Brian W.
Gleason, Nevada State College.)

· Page
92, part (c). Replace *a* = 0 with *x* = 0. (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

·
Page 94, Figure 10.3. The function should
be *f*(*x*,*y*) in the caption. (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

·
Page 101, Exercises 1 and 2 (b). These
problems should include the direction to evaluate the limit at (0,0) along these paths. (Reported by Jon
Barker, St. Ignatius High School, Cleveland,
OH.)

·
Page 107, Figure 10.11. The caption should
have *f*(*x*,*y*) = *xy*^{2}/(*x*+1). (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

·
Pages 109-110. In Activity 10.6 the
ordered pairs at which the wind chill is being evaluated in parts (a)-(e) are
all reversed (for example, part (a) should read *w _{v}*(20,-10)). (Reported
by Brian W. Gleason, Nevada State
College, found by his students.)

·
Page 113, Exercise 1 (c). Estimate *I*(90, 78), not *I*(78, 90). (Reported by Jon
Barker, St. Ignatius High School, Cleveland,
OH.)

·
Page 114, Exercise 2 (e). The word “given”
is missing in “Often we are given certain graphical information about a
function instead of a rule.” (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

·
Page 114, Exercise 3 (c). The point should
be (1,3) rather than (3,1). (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

·
Page 114-115. Delete Exercise 3 (e) (this
is actually a solution to Exercise 2 (e)). (Reported by Jon Barker, St. Ignatius High School, Cleveland,
OH.)

·
Page 115, Exercise 4 (b). Find parametric
equations for the tangent line to the trace at *x*
= 2. Exercise 4 (c). Find parametric equations for the tangent line to the
trace at *y* = 1. (Reported by Jon Barker, St. Ignatius High School, Cleveland,
OH.)

·
Page 117. Figure 10.18 has
the left hand, vertical axis labeled *f*(*y*,150) when it
is supposed to be *f*(150,*y*). (Reported by Rachael Sharp, Nevada State College.)

·
Page 117. The line - *f _{xy}*
= (

·
Page 118. The sentence beginning with “However,
to find the second partial derivative” ends incorrectly by interchanging the
order of the variables *x* and *y*. (Reported by Brian W. Gleason, Nevada State
College.)

·
Page 120, Activity 10.9. Throughout this
activity, the *x* coordinate should be
1.75 and the *y* coordinate -1.5.
(Reported by Jon Barker, St. Ignatius High
School, Cleveland, OH.)

· Pages
121-122, Activity 10.10. Part (a) has *w _{TT}*(-10,20) when it should be

*w _{T}*(15,-10)
instead of

· Page
124, Exercise 2 (b) and (c). These two parts ask the same thing. Remove part
(b) and replace *I _{TH}*(94,
75) with

·
Page 131, Activity 10.12 (c). This part of
the problem should ask to estimate *f*(2.2, 1), *f*(2, 0.8), and *f*(2.2, 0.8). (Reported by Jon Barker, St.
Ignatius High School, Cleveland, OH.)

· Page 131, Activity
10.13 (a). It is probably more intuitively to assume that *x* and *y *are measured in
miles in the easterly and northerly directions, respectively. Also, the point
(3, 1) is missing in *h _{y}*(3, 1).
(Reported by Jon Barker, St. Ignatius High
School, Cleveland, OH.)

·
Page 144, Exercise 3 lists two
equations for *x* when the latter one
should be for *z*. (Reported
by Brian W. Gleason, Nevada State
College.)

· Page 145, Exercise
6 in Section 10.5. The problem switches from ``she'' to ``his''. More
importantly, since no parameterization is given for the intersection of the
surfaces there could be many different answers to the problem as stated. In
future versions this problem will contain two parts: (a) Show that *x*(*t*) = 4cos(*t*) and *y*(*t*) = 4sin(*t*) is a parameterization of the ``shadow'' of the curve that is the
intersection of the graphs of *f* and *h* that lies in the *x*-*y* plane. (b) Use the
parameterization from part (a) to find the instantaneous rate at which her
height is changing with respect to time at the instant t = 2π/3. (Reported
by Brian W. Gleason, Nevada State
College.)

· Page 145, Exercise
7 in Section 10.5. The resistance formula should be 1/*R* = 1/*R*_{1} +1/*R*_{2}. (Reported by Brian W. Gleason, Nevada State College.)

· Page 163, Example
10.2. The last sentence states “We then consider *f _{xx}*(0,0) = 2 < 0 …” which should, of course, be

· Page 213, Exercise
1. Parts (a) and (b) both ask for the mass. Part (a) should ask for an iterated
integral and a sketch of the region, while part (b) should ask for the mass of
the plate. (Reported by Brian W. Gleason, Nevada State
College.)

· Page 240, Exercise
3. Part (c) should ask to set up iterated integrals using all possible orders
of integration. (Reported by Brian W.
Gleason, Nevada State College.)

Last updated 12/11/15.