Principles of Analysis

Homework Assignment #11 (LAST Assignment!)

Due Monday, April 29, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

Section 5.4
State and prove both parts of the Fundamental Theorem of Calculus. The proof should be in your own words, modeled after the proof from class and/or the text.

Section 6.1
Problems:   1c, 1f, 3a, 3e, 4a, 4b, 8 (parts a, b, e, g, i)

Hint: In problem #1, use ONLY the definition of convergence of an infinite series. Try computing some partial sums or writing out a few terms of the series. For problem #8i, try using the limit comparison test with a very special series.

Section 6.2
Problems:   1 (parts a, b, e), 4 (parts a, b, e), 11a, 11b

Hint: For problem #1e, you may use the inequality ln(n) < n. For problem #11a, apply Theorem 6.1.4 to the first series in order to bound |a_n b_n|.

Section 6.3
Problems:   1 (parts a, b, f), 7a, 7b

Hint: For problem #7b, start with the power series expansion for 1/(1-x^2) (it's a geometric series), then integrate both sides. You will need to use partial fractions.