MATHEMATICS 120 PROBLEM SET 10
Due November 27, 2002
For full credit, please show all work.
1. (5 marks) If f (x) is a twice differentiable function such that f (3) = 1, f 0 (3) = 1.5, and
−2x ≤ f 00 (x) ≤ −x for all x > 0, find the smallest interval you can that contains f (3.2).
2. (5 marks) Prove that if f (x) is an even function such that f (n) (x) exists everywhere
for all n, then all its Taylor polynomials Pn (x) about x = 0 are also even.
3 and 4. (10 marks) End of the year: everybody gets 10 marks for free!
Please read Sections 4.7-4.9 of the textbook. The recommended practice problems are:
Section 4.7, 1–30; Section 4.8, 1-25; Section 4.9, 1–32.
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