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.

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· 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 2b. (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(πs/4) causes the curves to intersect at (2,0,1). In future editions the curves will be changed to r(t) = 〈t + 1, cos(πt/2), 1/(1+t)〉 and w(s) = 〈s², sin(πs/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) = (x² + y²)^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) = xy²/(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 = (f_x)_y, and evaluate f_xy(150, 0.6) - should not appear at the end of part (c).

· 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_TT (20, -10) as the value to be estimated. Part (e) also refers to w_TT (-10,20) when it should be w_TT (20, -10). (Reported by Brian W. Gleason, Nevada State College.) Part (c) should have

w_T(15,-10) instead of w_T(30,-10). (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

· Page 124, Exercise 2 (b) and (c). These two parts ask the same thing. Remove part (b) and replace I_TH(94, 75) with I_HH(94, 75) in part (c). (Reported by Jon Barker, St. Ignatius High School, Cleveland, OH.)

· 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/R₁ +1/R₂. (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 f_xx(0,0) = 2 > 0. (Reported by Brian W. Gleason, Nevada State College.)

· 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.