Spielberg MAT 371 SPRING 2004
HOMEWORK ASSIGNMENTS
Week 6
Read sections 3.3 (skip 3.19, 3.20, 3.23 and following), 3.4 (skip 3.29, 3.30)
Problems, due Wednesday, 3/3:
•3.1 # 29, 35b
(In 3.1 # 29, the wording may seem ambiguous. You can replace it with the
following: Suppose that fhas both one-sided limits at each point of [a, b]. Prove
that fis bounded on [a, b].)
•3.2 # 4, 16
•Let I⊆Rbe an interval, and let f,g:I→Rbe continuous functions. For
x∈Ilet h(x) = maxf(x), g(x). Prove that his continuous on I.
•3.3 # 7
Week 7
Read sections 4.1-2
Problems, due Friday, 3/12:
•3.3 # 15, 22
•Let f:R→Rbe continuous. Prove the impossibility of the statement: for every
point cin the range of f, the equation f(x) = chas exactly two solutions.
•3.4 # 2d, 3, 8 (In problem 8, do not use theorems 3.29 or 3.30.)
Test 2 will be given in class on Monday, 3/8. (Note that this is a change from the date
originally given in the syllabus.) It will cover chapter 2 and chapter 3, sections 1-2.