Question

Chapter 8, Section 8.1, Question 032 3 5 This problem refers to the functio where the functio Inction g (x) = 1 + 3x + x + Fax is used to approximate the values of 1 + -X + is used to approximate the values of f(x) = x Evaluate f (x) and g(x) at x = 0.1, 0.2, 0.3 and record your answers to three decimal places in a table. Does your table support the claim that g(x) gives a good approximation to f (x) for these values of x ? 0.1 0.2 0.3 f (x) 8(x) the claim that g(x) gives a good approximation for f (x) for values of x. Yes. The table does support No. The table does not support

Answer 1

16 0.2 8(x) = 1 + 2x + 3x + 23 a f(n) - - Now, $(0-1) - Voeg 1.054 f(0.2) - 10.2 - Joe = 1.118 f(0-3) Vios 1.195 and a (0-1)= 1+ + 3000 + 50cm) - 1.054 f (0-2) - + 02 +33(0.04) + 5(0.008). 1.118 g (0.3) = 1 + 0.3 + 3 (0.00) + 510.027 21-192 xo 0.3 f(x) 1.054 1.118 11.195 gen) 1.192 1.054 118 oor Here, f(0.2) - f(0.1) = g(0.2) - 9(0.1) - 0.064 but, $10.3) - + (0.2) = 0.097 and, g (0.3) - 9(0.2) = 0.074 Ar g(0.3) - g (0.2) <f(0.3) - +(0.2), ro, we have to complete less iteration for og and so, ger) be converge quickly. So, yes, the table does support that g(x) gives a good approximation for fex) for valeces of X.