The M1M1 treasure hunt, week 2
Welcome to the 2014-15 M1M1 treasure hunt!
This quiz is not for course credit, but I hope it will be fun. Each week I shall produce a page such as this with a number of questions relating to the course. Entering the correct answers (in any order) will automatically decrypt a message giving a clue to the mystery M1M1 treasure.
Note: The Hunt takes the role of the "starred questions" on the problem sheets for M1M1 - it is intended that you might discuss the questions with your Personal Tutor and/or your peer group tutors.
Type the answer to each question in the box below it - you will be told whether each answer is right or not. When all answers are correct, you will receive the first of the treasure clues.
(1) What is the maximum value attained by the odd part of the function sin(x3+1)]?
(2) The function f(x) = x log(x) -2x is defined for 0 < x ≤ a. What is the largest value of a for which f(x) is invertible on this domain?
(3) A few years ago, I asked the class to find functions f(x) and g(x) such that the product f(x)g(x) was an odd function and the sum f(x) + g(x) was an even function. I received the answers:
(a) f(x) = cos x + sin x, g(x) = cos x - sin x
(b) f = 1, g = 3
(c) f = 0, g is any even function
(d) f = x + 1, g = x2 - x
(e) f(x) = g(-x), g is any function
Write the letters corresponding to any correct answers in the box in alphabetic order. If you guess that none is correct write "I am lazy" in the box. If, after consideration, you think none is correct, write "I am not lazy" in the box.