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MA121, Homework #5 due Thursday, Feb. 5 in class 1. Compute each of the following integrals: Z 8x − 5 dx, 2 2x − 3x + 1 Z log(x2 − 1) dx. √ 2. Define a sequence {an } by setting a1 = 1 and an+1 = 2an + 1 for each n ≥ 1. Show that 1 ≤ an ≤ an+1 ≤ 3 for each n ≥ 1, use this fact to conclude that the sequence converges and then find its limit. 3. Compute each of the following integrals: Z x2 sin x dx, Z sin(log x) dx. • You are going to work on these problems during your Friday tutorials. • When writing up solutions, write legibly and coherently. Use words, not just symbols. • Write both your name and your tutor’s name on the first page of your homework. • Your tutor’s name is Thomas, if you are a TP student; otherwise, it is Pete. • Your solutions may use any of the results stated in class (but nothing else). • NO LATE HOMEWORK WILL BE ACCEPTED.