Question

8. Use Taylor's Theorem to show that the approximation f 8 f(x+h) - 8f(x – h) - f(x+ 2h) + f (x – 2h) 12h is (h4). # Approximate f'(1.05) using h=0.05 and h = 0.01 in equations (2) and 4). Use the following data: x 1.0 1.04 1.06 1.10 f(x) 1.6829420 1.7732994 1.8188014 1.9103448 | Based on the definition of the derivative, for small values of h, we have the following estimate (forward difference) for the derivative at some value x: f'() f(x+h)-f(x) (2) Consider now the method (central difference) given by f'(x)=f(x +h) – f(x – h) 10 Approximate f"(1.3) using h=0.05 and h = 0.005 in equation (9). Use the following data: * 1.20 1.29 1.30 1.31 1.40 Rx) 11.59006 13.78176 14.04276 14.30741 16.86187 is some value in the interval between x - 2h and x + 2h. Solving for the 2nd derivative term we where get f"(x) = 442\x(x + 2h) – 2f(x) + f(x – 2h) "*°•

please need help on 8, 9 and 10

Answer 1

By rules and regulations we are allow to do only one question at a time..so i do only question 8th ..

Doubt in any step then comment below.. i will help you..

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