Unformatted text preview: below an error criterion conforming to two significant figures. 3. a) Use 0 – 4 th order Taylor series expansions to predict f(3) for f(x) = ln(x) using a base point of x = 1. Calculate the true percent relative error for each approximation. Assume the value of f(3) calculated by your calculator / computer is the true value. b) Repeat the above calculation for f(1.5). c) What do you observe about the error in the above calculations and what can you conclude about the convergence of Taylor series approximations? 4. Evaluate and interpret the condition number for a) x e ) x ( f − = for x = 9 b) ) x cos( ) x sin( ) x ( f + = 1 for x = 1.001 π c) x e ) x ( f x 1 − = for x = 0.01...
View Full Document
- Spring '10
- Taylor Series, percent relative error, significant figures. sin