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ASSIGNMENT 3 There are two parts to this assignment. The first part consists of 15 questions on WeBWorK — the link is available on the course webpage. The second part consists of the questions on this page. You are expected to provide full solutions with complete justifications. You will be graded on the mathematical, logical and grammatical coherence and elegance of your solutions. Your solutions must be typed, with your name and student number at the top of the first page. If your solutions are on multiple pages, the pages must be stapled together. Your written assignment must be handed in before the start of your recitation on Friday, January 30. The online assignment will close at 9:00 a.m. on Friday, January 30. Z 4 Z f (t) dt = −20. Evaluate 1. Let f (t) be continuous, with 0 2 f (2t) dt. 0 2. Find all continuous functions f (t) such that Z 1 2 2 1 Z f (t ) dt = 0 0 1 f (t) dt − . 3 (Hint: write the integrals in terms of the same variable.) 3. (a) Let f (t) be continuous. Prove that Z a Z 0 for any constant a. Z π t sin(t) π2 (b) Prove that dt = . 2 4 0 1 + cos (t) a f (a − t)dt f (t)dt = 0