MATH 152 Final: MATH152 MATH152 FinalD

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31 Jan 2019
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You may use this page for any answer(s) which you could not t in the space provided. If using this page, clearly indicate the question number(s) beside your answer(s). Also indicate on the question page that your answer is on page 0. Failure to do so will result in deduction of marks. You do not need to justify your answers. [2] (a) z csc2 x dx = cot x. [2] (b) the second degree taylor polynomial for f (x) = ex centred at a = 1 is e+ex+ex2. [2] (c) the length of the cardioid r = 1+sin is given by the integral z 2 . 2 + 2 sin d . (it is given that the full length of the cardioid is given by the interval 0 2 . ) [2] (d) x2 + sin y = 5 is a solution to the di erential equation.

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