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)

6.1 #7. Graph does not cross the x axis at the point given in their answer.

Question 21 from section 6.1 says it's a positive +1 to infinity for the range, which is incorrect because it should be from -1 to infinity. The negative under the square root computes a zero, which is included in the range.

6.1 # 58. Did not define the variable C.

6.2 question 50, the integral for arc length does not appear to be computable in closed form.  An exact answer is not possible, nor is an approximation asked for. 

In 6.4 question 4, they are multiplying the integral by 3/2 but it should be multiplied by 32.