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1. hw 6 (1) Read section 11.1 of the book by Stewart.
(2) Use definition to prove that lim
n→∞
3n2− n − 1 5n2+ 4n + 3 = 3
5. (3) Suppose that 0 < a < b. Define xn by
xn = √n
an+ bn, n ∈ N.
Find lim
n→∞xn.
(4) Let b > 0 and an= bn/n! for n ∈ N. Prove that the sequence (an) is convergent and find its limit.
(5) Do Exercise : 34, 70, 80, 81, 86, 89, 90, 91, 92
1
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