# Errata List for Integrated Calculus

Last updated Oct. 20, 2004

It may seem that there are an awful lot of errors reported here, but in my defense I offer this modification of a famous quote by Walter Mondale: Other calculus books are full of typos, and so is mine. They won't tell you about it; I just did.

### Chapter 0

• Section 0.1, page 7, Figure 0.5: The "dot" at 0 should be closed, not open; in other words, the interval being shown is supposed to be [0,infinity).

• Section 0.2, page 17, end of first paragraph: Change "x^2 - 1 = 0" to "x^2 + 1 = 0."

• Section 0.2, page 18, last sentence before Example 0.10: Change "multiplying out the left-hand side" with "multiplying out the right-hand side."

• Section 0.2, Exercise 88: The way the problem is written there are no real solutions. Change the perimeter from 38 inches to 44 inches.

• Section 0.3, page 31, last paragraph: Change "the solution to x^2 <= c" to "the solution to x^2 <= c^2". (I'm using "<=" here to represent the "less than or equal to" symbol.)

• Section 0.3, answer to Exercise 48 should be: [3/2,infinity).

• Section 0.3, answer to Exercise 50 should be: [1/3,infinity).

• Section 0.3, answer to Exercise 76 should be: (-infinity,-1.316] U (-1,1.316]. (Note "U" for union symbol.)

• Section 0.4, answer to Exercise 28: Add a closing quotes symbol to the end of the statement.

• Section 0.4, answer to Exercise 60: Add a closing quotes symbol to the end of the statement.

### Chapter 1

• Section 1.1, answer to Exercise 10: Add "Range(f) = S" to the end of the answer to part (a).

• Section 1.1, answers to Exercise 12 and 13: Add "One possible answer is" to the answers to parts (a), (b), and (c).

• Section 1.1, answer to Exercise 18: Change to "One answer is f(person) = 42. The range of this function is {42}. No identity functoin from P to R is possible." (Note use of R for the real numbers.)

• Section 1.1, Exercise 41: Replace "the surface area of a cubical room" with "the area of the walls, given that the room is cubical in shape."

• Section 1.2, answer to Exercise 28 should be: roots at x = -1 and x = 3, y-intercept at y = -3.

• Section 1.4, answer to Exercise 50: replace "4 < t <= 6" with "4 < t < 6". (Note use of "<=" for "less than or equal to".)

• Section 1.5, page 98: Omit the second sentence in the introductory paragraph. (Inverses won't be covered until Section 1.7 in this book!)

• Section 1.5, page 99: In the last centered line of Example 1.48, change "3" to "2", three times.

• Section 1.5, Exercise 33: Change the domain of f to [2,infinity). (Otherwise part (b) of the problem is not true.)

• Section 1.6, page 113: In the first sentence of the second paragraph of Example 1.63, replace "independent variable" with "dependent variable."

### Chapter 2

• Section 2.2, sentence after Statement (2) refers to Statement (1), but should refer to Statement (2).

• Section 2.2, answer to Exercise 57 should be: 5.

• Section 2.3, Exercises 17 and 34: Replace "lim_{x --> 1} 1/x = 1" with "lim_{x --> 2} 1/x = 1/2."

• Section 2.4, page 174, the sentence just before Example 2.35: Replace "The product, quotient, and reciprocal rules" with "The product and quotient rules".

• Section 2.5, page 183, third line of the solution to Example 2.41(b): Replace "1 + 1 = 0" with "-1 + 1 = 0".

• Section 2.5, instructions above Exercises 41-44: Change "find a real number a such that" to "find all real numbers a (if any) for which", and remove the "(if possible)" from the end.

### Chapter 3

• Section 3.1, page 229: replace "Table 10.3" at the bottom of the page with "Table 3.1".

• Section 3.1, page 230: replace "Table 10.3" with "Table 3.1" three times on this page.

• Section 3.1, instructions above Exercises 84-89: replace "Table 10.3" with "Table 3.1".

• Section 3.3, Exercise 3: The function described in this problem does not exist. Change the conditions to: lim_{x --> 0+} f(x) = -1, lim_{x --> 0-} f(x) = 1, f(0) = -1. (Note this has only two limits, not four as in the original problem.) Then change the answer to (a) no (since not continuous at x = 0), (b) no.

• Section 3.3, Exercise 4: Add the condition f(1) = 3 after the four limits.

• Section 3.3, answer to Exercise 14, add to the end of the answer: Not differentiable, and not left or right differentiable, at x = 1.

• Section 3.3, instructions for Exercises 22-24: replace "graphing calculator the examine" with "graphing calculator to examine".

• Section 3.3, answer to Exercise 25(a): the first limit should have answer 1, not -1.

• Section 3.7, Exercise 39: The problem number should be printed in black, not red (no answer in the back).

• Section 3.7, Exercise 40: The problem number should be printed in red, not black (answer is in the back).

• Section 3.8, Exercise 8: Change "some function" to "some differentiable function".

• Section 3.8, answer to Exercise 52: replace "x - 1" in the denominator with "(x - 1)^2".

### Chapter 4

• Section 4.2, answer to Exercise 42: The second limit should have "x --> 1^-", not "x --> 0^-". (Note use of "-->" for arrow.)

• Section 4.3, answer to Exercise 17: Replace "3(h)^(-1)" with "3(3+h)^(-1)" in the numerator.

• Section 4.4, answer to Exercise 29 should be: "Even; f(-x) = f(x)."

• Section 4.5, answer to Exercise 71: change "-f(-x)" at the end of the second-to-last sentence to "-f(x)".

### Chapter 5

• Section 5.2, answer to Exercise 43 should be: 360.

• Section 5.2, answer to Exercise 53: Replace "71/10" at the end with "2".

• Section 5.3, answer to Exercise 48 should be: f(x) = x^2 - 4x + 6.

• Section 5.4, answer to Exercise 22 should be: At t = 3.21515 minutes; at t = 1.4514 minutes.

• Section 5.4, answer to Exercise 35: Add "(a)" before the first sentence and "(b)" before the second sentence (to label parts of the problem).

### Chapter 6

• Section 6.2, answer to Exercise 39: Replace "x = 5" with "x = -5".

• Section 6.2, answer to Exercise 56: Add "vertical asymptote at x = -1" to the list of characteristics.

• Section 6.4, answer to Exercise 26: At end of first sentence, change "y = x" to "y = x + 1".

### Chapter 7

• Section 7.1, answer to Exercise 23: Delete the first limit given (not asked for in the problem).

• Section 7.4, answer to Exercise 28: Replace "36 pi" in the denominator with "72 pi". (Note using "pi" for the Greek letter "pi" that I can't type here, of course.)

• Section 7.5, answer to Exercise 52: Replace "x = 3" with "x = 2".

• Section 7.5, answer to Exercise 64: Replace "5.4288" with "6.86979" and "2.7144" with "1.853".

• Section 7.5, answer to Exercise 65: Change the radius answer to "2(10/pi)^(1/3) == 2.942", and the height answer to "(10/pi)^(1/3) == 14.710" (using "pi" for the greek letter and "==" for the "approximately" symbol).

• Section 7.5, answer to Exercise 68: Change "200" to "200 square units".

• Section 7.5, answer to Exercise 70: Add "for 625 feet" to the end of the sentence.

### Chapter 8

• Section 8.3, answer to Exercise 41 should be negative infinity, not positive infinity.

• Section 8.5, answer to Exercise 42 should be: "Domain is (-infinity,0], always decreasing and concave down, lim_{x --> -infinity} f(x) = 1 (so f(x) has a horizontal asymptote at y = 1)."