Math 192 Review Problems for Final Exam
The nal exam will be cumulative, and the problems below are only samples of some of the types of problem which may be asked on the nal. You should also study the review sheets for the two midterms, as well as your l
Review problems for the rst midterm 1. Exercises 37 and 38 in Chapter Review Exercises of Chapter 6 (pp. 414-415. For these problems also set up denite integrals for the volume obtained by rotating the given region about the axes y = 2 and x = 3c. (Dont e
Solutions to selected review problems
These solutions focus on problems on the review sheet that we did not discuss adequately in class.
2. (b) When x is large x2/3 is the dominant term in the numerator of the integrand.
1
Therefore we expect the integral
Formula Sheet for the second Midterm Exam 1. Let Tn (x) be the Taylor polynomial centered at a for f . Then 1 Rn (x) = f (x) - Tn (x) = n!
x
(x - u)n f (n+1) (u) du.
a
2. Suppose that cfw_an and cfw_bn are positive sequences. an (a) If 1 bn converges an
Review Problems for the first Midterm 1. Determine whether the improper integral converges and, if so, evaluate it.
a)
1
e x dx x
2
b)
1
1 dx x ln x
c)
1
xe-2x dx
2. Use the comparison test to determine whether the integral converges.
a)
1
1 dx 7 + 2x + 1
Formula Sheet for the first Midterm Exam Error bounds: Let f be a given function on the interval [a, b]. Let K2 be an upper bound on the values f (x) for x [a, b], and let K4 be an upper bound on f (iv) (x) for x [a, b]. Let Mn , Tn , and Sn denote respec