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PS1_ChE 230_assign_10

# PS1_ChE 230_assign_10 - below an error criterion conforming...

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ChE 230 – Spring 2010 Problem Set 1 – 1/12/10-1/19/10 1. The velocity ( V ) of a falling parachutist as a function of time ( t ) can be calculated using the equation ) e ( c gm ) t ( V t ) m / c ( = 1 where c is the drag coefficient, g = 9.8 m/s 2 is the acceleration due to gravity, and m is the mass of the parachutist. If m = 50 kg and c = 12.5 ± 2 kg/s. Determine the uncertainty in V (i.e., the propagated error) for a time of t = 6 s. 2. The Maclaurin series expansion for sin(x) is ..... ! x ! x ! x x ) x sin( + + = 7 5 3 7 5 3 Starting with the simplest approximation [ sin(x) = x ] add terms one at a time to estimate the value of sin( π /4). Use your calculator or computer to obtain the true value. For each approximation calculate the true and approximate percent relative error. Continue to add terms until the absolute value of the approximate error falls
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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...
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