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ASSIGNMENT 1

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There are two parts to this assignment. The first part is 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 arguments and justifications. You will be graded on the correctness, clarity and elegance of your solutions. Your answers must be typeset or very neatly written. They must be stapled, with your name and student number at the top of each page.

1. Suppose an isosceles triangle has perimeter 10 cm. Find an expression for its area A as a function of the length of its base b (assume that the other two sides are the sides of equal length). What is the domain of A ?

2. (a) The Ladner Clock Tower is the large tower west of the Barber Library. Determine its height directly

(that is, by taking some kind of measurement, not by Googling it). Make sure to explain your method.

(b) Propose a function describing the length of the shadow cast by the Ladner Clock Tower from dawn to dusk on Monday, September 17, 2012. Justify your answer mathematically and sketch its graph.

3. A function f has a fixed point at a if f ( a ) = a . For example, f ( x ) = x 2 a function of the form f ( x ) = ax 3 + bx 2 has fixed points at 0 and 1. Find

+ cx + d which has fixed points at 1, 2 and 3. There are a number of ways to solve this problem; bonus marks will be given for particularly elegant solutions.