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Analysis Homework #1 due Thursday, Oct. 21 1. Determine max A when A = {y ∈ R : y = −3x2 + 2x − 1 for some x ∈ R}. n−1 2. Show that the set B = { 2n+1 : n ∈ N} has no maximum. n−1 3. Show that the set B = { 2n+1 : n ∈ N} is such that sup B = 1/2. 4. Show that the set C = {x2 : x ∈ R} has no upper bound. Hint: if y is an upper bound, then y ≥ y 2 and y ≥ 4 > 1. • You are going to work on these problems Friday in class. • When writing up solutions, write legibly and coherently. Use words, not just symbols. • Write your name and then MATHS/TP/TSM on the first page of your homework. • Your solutions may use any of the results stated in class (but nothing else). • NO LATE HOMEWORK WILL BE ACCEPTED.