436EX1F04 - MATH 436 Exam 1 SHOW ALL WORK x NAME 1 Let y =...

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 MATH 436 - Exam 1                NAME: _________________________   SHOW ALL WORK 1) Let y = f(x) = x cos(.1  x e ) on the interval [0,  π ]. a) Find the 3rd Taylor polynomial P ) ( 3 x to f(x) centered at x = 2, and graph both f(x) and P ) ( 3 x on this interval. b) What is the total absolute error in this approximation on this interval? c) Graphically find the "largest" interval containing x = 2 so that this Taylor polynomial will  approximate f(x) with pointwise absolute error of at most .05. 2) Using the remainder formula, find the "smallest" order n so that the Taylor polynomial Pfor f(x) =  sin(2 x) centered at x = 0 will approximate f(x) on the interval [0, 2  π ] with pointwise absolute error in  this approximation of at most .03.
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3) Give some of the advantages and disadvantages of using the methods of Newton 1st order, 
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  • Spring '08
  • Ken
  • Math

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