MATA30H3 Final: MATA30 Final Exam 2012 Winter
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MATA30H3 Full Course Notes
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Do not open this booklet until instructed to do so. Notes: no calculators, or any electronic aid is permitted. It is your responsibility to ensure that, at the start of the test, this booklet has all its pages. Please leave all the pages of this booklet stapled. Do not remove any pages: answer all questions in the space provided. Show your work and justify your answers for full credit. Mata30h3 page 1: [12 marks] evaluate the given limits: x2 sin(cid:18) 1. Ln x arctan sin t dt: [20 marks] consider the function f (x) = Make a table. int* f (x) f (x) f (x) conc. (*int = intervals) (*conc. =conclusion) (k) sketch a graph of f (x) Mata30h3 page 2: [10 marks] use reimann sum and sums of positive integers to nd the area under the curve f (x) = x2 1 on [2, 4].