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.