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6.1 Introductory Calculus • 215err_x := 1120 (−sin(ξ) esin(ξ) + 16 cos(ξ) 2 e sin(ξ)− 15 sin(ξ) 2 e sin(ξ) + 75 sin(ξ) cos(ξ) 2 e sin(ξ) − 20 cos(ξ) 4 e sin(ξ)− 15 sin(ξ) 3 e sin(ξ) + 45 sin(ξ) 2 cos(ξ) 2 e sin(ξ)− 15 sin(ξ) cos(ξ) 4 e sin(ξ) + cos(ξ) 6 e sin(ξ) )(x − π) 5> err_xi := diff(err, xi);err_xi := 1720 (−cos(ξ) esin(ξ) − 63 sin(ξ) cos(ξ) e sin(ξ)+ 91 cos(ξ) 3 e sin(ξ) − 210 sin(ξ) 2 cos(ξ) e sin(ξ)+ 245 sin(ξ) cos(ξ) 3 e sin(ξ) − 35 cos(ξ) 5 e sin(ξ)− 105 sin(ξ) 3 cos(ξ) e sin(ξ) + 105 sin(ξ) 2 cos(ξ) 3 e sin(ξ)− 21 sin(ξ) cos(ξ) 5 e sin(ξ) + cos(ξ) 7 e sin(ξ) )(x − π) 6The two partial derivatives are zero at a critical point.> sol := solve( {err_x=0, err_xi=0}, {x, xi} );sol := {x = π, ξ = ξ}The error is zero at this critical point.> eval( err, sol );0You need to collect a set of critical values. The largest critical valuethen bounds the maximal error.> critical := { % };critical := {0}The partial derivative err_xi is zero at a critical point on either ofthe two boundaries at x = 2 and x = 4.> sol := { solve( err_xi=0, xi ) };
216 • Chapter 6: Examples from Calculussol := { 1 π, arctan(RootOf(%1, index = 4),2RootOf(_Z 2 + RootOf(%1, index = 4) 2 − 1)), arctan(RootOf(%1, index = 1),RootOf(_Z 2 + RootOf(%1, index = 1) 2 − 1)), arctan(RootOf(%1, index = 5),RootOf(_Z 2 + RootOf(%1, index = 5) 2 − 1)), arctan(RootOf(%1, index = 2),RootOf(_Z 2 + RootOf(%1, index = 2) 2 − 1)), arctan(RootOf(%1, index = 6),RootOf(_Z 2 + RootOf(%1, index = 6) 2 − 1)), arctan(RootOf(%1, index = 3),RootOf(_Z 2 + RootOf(%1, index = 3) 2 − 1))}%1 := −56 − 161 _Z + 129 _Z 2 + 308 _Z 3 + 137 _Z 4+ 21 _Z 5 + _Z 6> evalf(sol);{−1.570796327 + 0.8535664710 I, 1.570796327,−0.3257026605, −1.570796327 + 2.473801030 I,0.6948635283, −1.570796327 + 1.767486929 I,−1.570796327 + 3.083849212 I}You should check the solution set by plotting the function.> plot( eval(err_xi, x=2), xi=2..4 );0.60.40.20–0.22.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4xi
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Learning Guidecommand the brillianc
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ii•Waterloo Maple Inc.57 Erb Stre
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iv • ContentsThe numer and denom
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vi • ContentsThe Parts of an Expr
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viii • Contents
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2 • Chapter 1: Introduction to Ma
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98 • Chapter 4: Graphics> f := x
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100 • Chapter 4: Graphics> plot(
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102 • Chapter 4: GraphicsFigure 4
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104 • Chapter 4: Graphics0.40.2-1
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270 • Chapter 7: Input and Output
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288 • Chapter 8: Maplets8.2 Termi
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294 • Indexexact, 8finite rings a
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296 • Indexspherical, 114viewing,
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298 • IndexXML, 283ExportMatrix,
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300 • IndexHP LaserJet, 284HTML,
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310 • Indexunordered lists (sets)
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