MATH 387 Midterm: MATH387 Winter 2010 Exam
31 Jan 2019
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Instructions: all questions carry equal weight, answer 5 or 6 questions; credit will be given for the best 5 answers, answer questions in the exam book provided. Start each answer on a new page: this is a closed book exam, notes and textbooks are not permitted, non-programmable calculators are permitted, translation dictionaries (english-french) are permitted. This exam comprises of the cover page, and 2 pages of 6 questions. Show that if g is p-times di erentiable with g(x ) = x and g (x ) = g (x ) = . = g(p 1)(x ) = 0 then the sequence xn so de ned is convergent of order p. (c) find m so that newton"s method applied to f (x) = (x2 a)xm converges (at least) cubically to a. , xn] = f (n)( ) n! (d) given that pn(t) which interpolates at x0, x1, .
