|© | Dror Bar-Natan: Classes: 2004-05: Math 157 - Analysis I:||(27)||
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Solve 4 of the following 5 problems. Each problem is worth 25 points. If you solve more than 4 problems indicate very clearly which ones you want graded; otherwise a random one will left out at grading and it may be your best one! Write your answers in the space below the problems and on the front sides of the extra pages; use the back of the pages for scratch paper. Only work appearing on the front side of pages will be graded. Write your name and student number on each page. If you need more paper please ask the tutors. You have an hour and 50 minutes.
Allowed Material: Any calculating device that is not capable of displaying text.
Problem 1. Find formulas for , and in terms of . (You may use any formula proven in class; you need to quote such formulae, though you don't need to reprove them).
Problem 3. A function is defined for and has the graph plotted above.
Problem 5. Give examples to show that the following definitions of do not agree with the standard one: