MATH 230 Final: Final spring 2013
15 Feb 2019
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Instructions: show all of your work on the pages provided! Explain your reasoning using complete sentences and correct grammar, spelling, and punctuation. All numerical answers must be exact; e. g. , you should write instead of 3. 14, 2 instead of 1. 414, and 1. Make sure that your nal answer is clearly indicated. Check to make sure you have pages 1 - 15. Calculators, course notes, textbooks, etc. are not allowed. Do not write your name on this exam! Write your netid and your student id number in the spaces provided at the top of this page. P and q passes through the center of the sphere1. Find the point q on the sphere such that (6, 2, 3) and q are antipodal points. 1on the earth, the north and south poles are antipodal points. For each of the following, explain why the limit does or does not exist.
