|Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I:||(97)||
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Solve the following 5 problems. Each is worth 20 points though in question 4 you may earn a 5 points bonus that brings the maximal possible total to 105/100. 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. Compute the following definite and indefinite integrals in elementary terms:
Problem 2. The ``unit ball'' in is the result of revolving the domain (for ) around the axis.
Problem 3. Let be a real number which is not a positive integer or 0, let and let be a positive integer.
Problem 4. Let be a ``sequence of sequences'' (an assignment of a real number to every pair of positive integers) and assume that is a sequence so that for every we have . Further assume that .