222 Textbook Errata

These are the mistakes that students have already found.  Please check here before sending me one.

I found an error in section 0.5 in the grey box labeled Substitution with Indefinite Integrals. The problem states Let u =g(x),, where g'(x) is continuous over an interval... There are two commas after g(x) at the beginning of the sentence where there should only be one.

I found a second error, this time a mathematical error in the textbook. The problem is located in section 0.6 in example 0.6.4:Finding a Price-Demand Equation.  In this problem, in the very last step, 100 is supposed to be plugged into p(x) to solve for the price. When the author solved the problem the -0.01(100) was brought down from the exponent. This changed the problem to become p(100) = 1.5e - 0.01(100) + 1.44 = 1.99. If you were to plug the exact problem they wrote for p(100) the value is $4.517. However, if you properly plugged 100 in for x in the exponent shown in p(x) the equation would then be p(100) = 1.5e^(-0.01(100)) +1.44 = 1.99.  Which when solved does indeed give you $1.99.

In question 60 of the exercises  for0.6 the question asks for you to compute the integral of an equation from N to N+10, but in the answer this integral is shown going from N to N+1.

1.1 #21 It says one of the equations is x=y but on the graph it says x=2y.

1.1 Question 39 involves something we don't know how to do yet (integrating (1-x^2)^1/2).

In section 1.1 of the textbook, the answer to question #27 is wrong. After doing the calculations, I got an answer of e-2 units squared
and the textbook says the answer is e^-2 units squared. I think the textbook accidentally put the minus two as an exponent when that is not necessary for this problem.

Question 29 in 1.1 asks for the area between X=y^3+2y^2+1 and X=-y^2+1 but the graph it shows in the solution is the area between
X=y^3+2y^2 and X=-y^2+1  The graph in the written directions does not intersect in a way for the area between the curves to be found. The plus one in X=y^3+2y^2+1 is unwanted.

There is an unwanted parentheses after y=x^2. This can be found under 1.2E exercises 15.

1.3 #18, the answer says 32pi/5 but the answer is 32pi/4 which equals 8pi.

The exercises under section 1.3 in the textbook. For question #20, we do not yet know how to integrate xe^x.

Section 1.4 Question 33, the given solution is 120pi radical 26. My answer is 20pi radical 26. It seems as if they put an extra 1 in front of the answer.

The answer is incorrect for question 35 in section 1.4. The book got the ͏answer by forgetting to square the x in the surface area formula.  The correct integral is inaccessible to methods in Chapter 1. 

I’ve found an error with 1.4 question #37. The answer I got ͏was 15πsqrt(2) but the answer in the book is 9πsqrt(2).

In exercises under section 2.2 there is an error. For question #15, I got an answer ͏of -cos^3x/3 + 2cos^5x/5 - cos^7x/7 + c. This to me seems very different ͏from the answer provided in the textbook as they had completely different constants and angles in their answer.

I found an error in 2.6 question 35: they have 0.1544 as the answer, but it is 0.1554.

in problems for section 4.1, I disagree with the answer to question #7. If the previous term minus the current term equals 4 then the previous term must be 4 more than the next term. I then created a formula for an= -4n+1. The textbook answer is an= 4n-7.

Section 4.1 Question 11. Asks for an explicit formula for a(1)=0 and a(n)=2a(n-1)+1. The answer given is a(n)=2^n -1. When this explicit formula is used for terms of a(n) the values do not match that of the recursive formula from the initial condition.

In 5.2 question 3 the final answer is the summation of  (((-1)^(n+1)-1/(3n+1))x^n)I think it should be the summation of 
(((-1)^(n+1)-1/(3^(n+1)))x^n). 

I’ve come across an error with 3.1 #12. The equation given is not a valid solution to the given differential equation.  It is a solution to y' = 2xy. 

3.2 question 30 In the textbook they have the wrong values for the exact solution which they have 3 when it should be 4/3, and for the last x value they have 2.24 when it should be 1.24.

3.2 #38 y'=5t  y=-5/2t^2-2.  y(1)=-9/2 or -4.5. Book gives -0.5.  wrong actual value of y(1)