Past Exam for MTH 121 - Calc with Analytic Geom I with Bannon at Essex County College (ESSEX)

Exam Information

Material Type:Exam
Class:MTH 121 - Calc with Analytic Geom I
University:Essex County College
Term:Summer I 2005
  • Following Question
  • Either...or
  • Horizontal Tangent
  • Correct Answers
  • Decimal Places
  • Microsoft Word
  • Bonus Question
  • Mathematics
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Sample Document Text

MTH 121 - Summer - 2005 Essex County College - Division of Mathematics and Physics Bonus Question #5 1 - Printed June 7, 2005 Name: Signature: The following question is worth ten points total, and will be added to your second exam score. Only correct answers will be accepted. Due 06/16/2005.2 1. Use Newton's method to find the absolute minimum value of the function f (x) = x2 + sinx correct to six decimal places. Please trust the given graph, as it will help you determine if your final boxed answer is reasonable. Figure 1: Graph of f (x) = x2 + sinx. Solution: First, you need to find the first derivative. fprime (x) = 2x + cosx Now, you'll need to find where this derivative is zero. Looking at the graph, a good starting guess3 is x1 = ?0.43. Using Newton's method to find this solution to fprime (x) = 0, we have xn+1 = xn ? f prime (xn) fprimeprime (xn) = xn ? 2xn + cosxn 2?sinxn . 1This document was prepared by Ron Bannon using LATEX2?. Source and pdf are available by emailing a request ...

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