MATH 1070 Final: Math 1070 Final Exam
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Instructions: you may use a one page formula sheet. Formula sheets may not be shared: before you begin, enter your name in the space below, show all your work on the exam itself. If you need additional space, use the backs of the pages: you may not use books or notes on the exam. I: consider the equation e x = sin x. Find an interval [a, b] that contains the smallest positive root. Estimate the number of midpoints c needed to obtain an approximate root that is accurate within an error tolerance of 10 9. | cn| n + 1 . 2n+1 = 10 9, ln( 109) ln 2: prove that cn cn+1 = 2 n 2(b0 a0), where cn is the nth computed value of c in the bisection method. cn+1 cn = bn+1 an+1. 2 f (x) = 5x4 3x2, xn+1 = xn n x3 x5 n + 3.
