# 128ahw3sum10 - MATH 128A SUMMER 2010 HOMEWORK 3 SOLUTION...

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Chapter 11 / Exercise 1
Applied Calculus for the Managerial, Life, and Social Sciences
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MATH 128A, SUMMER 2010, HOMEWORK 3 SOLUTIONBENJAMIN JOHNSONHomework 3: Due Tuesday, July 62.3; 2, 12a, 192.4; 1b, 6b, 102.5; 1d, 6, 9section 2.32. Letf(x) =-x3-cosxandp0=-1. Use Newton’s method to findp2. Couldp0= 0 beused?
12. Use all three methods in this section to find solutions to within 10-7for the followingproblems.a.x2-4x+ 4-lnx= 0 for 1x2 and for 2x4
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Chapter 11 / Exercise 1
Applied Calculus for the Managerial, Life, and Social Sciences
Tan
Expert Verified
2BENJAMIN JOHNSONwith F(p) = -0.000000000Tolerance 1.0E-7For the Secant Method I used initial points 1.5 and 1.6, and 3.0 and 3.1:I Pn F(Pn)==========================================2 1.399400417 0.0246759883 1.414190660 -0.0033848134 1.412406598 -0.0000290515 1.412391154 0.0000000356 1.412391172 -0.000000000No of Iterations 6Approximation solution P = 1.412391172with F(P) = -0.000000000Tolerance 1.0E-7I Pn F(Pn)==========================================2 3.055647080 -0.0026006233 3.057067614 -0.0000642214 3.057103581 0.0000000555 3.057103550 -0.000000000No of Iterations 5Approximation solution P = 3.057103550with F(P) = -0.000000000Tolerance 1.0E-7For the Method of False Position, I used starting points 1 and 2, and 2 and 4;I Pn F(Pn)======================================2 1.590616109 -0.2965262613 1.455537328 -0.0789355294 1.422209961 -0.0183706445 1.414593610 -0.0041416476 1.412883592 -0.0009270407 1.412501187 -0.0002071698 1.412415747 -0.0000462809 1.412396661 -0.00001033810 1.412392398 -0.00000230911 1.412391446 -0.00000051612 1.412391233 -0.00000011513 1.412391186 -0.000000026No of Iterations 13Approximation solution P = 1.412391186with F(P) = -0.000000026Tolerance 1.0E-7
MATH 128A, SUMMER 2010, HOMEWORK 3 SOLUTION3