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The hyperbolic sine function is defined as (e - e¯³)/2. (a) Evaluate (e - e-ª)/2 at x = 0.05 on a 5 decimal digits machine. i. How large is the relative error? ii. How many significant decimal digits are lost?

The hyperbolic sine function is defined as (e - e¯³)/2. (a) Evaluate (e - e-ª)/2 at x = 0.05 on a 5 decimal digits machine. i. How large is the relative error? ii. How many significant decimal digits are lost?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. The hyperbolic sine function is defined as (eª - e-ª)/2. (a) Evaluate (e - e¯)/2 at x = 0.05 on a 5 decimal digits machine. i. How large is the relative error? ii. How many significant decimal digits are lost? (b) Evaluate e - e-ª on a binary machine where x > 0. What is the range of a to ensure at most 1 significant binary digit is lost? (c) Evaluate (e - e¯)/2 with fifth-order Taylor expansion (up to and including the x5 term). Give the general formula.
Transcribed Image Text:5. The hyperbolic sine function is defined as (eª - e-ª)/2. (a) Evaluate (e - e¯)/2 at x = 0.05 on a 5 decimal digits machine. i. How large is the relative error? ii. How many significant decimal digits are lost? (b) Evaluate e - e-ª on a binary machine where x > 0. What is the range of a to ensure at most 1 significant binary digit is lost? (c) Evaluate (e - e¯)/2 with fifth-order Taylor expansion (up to and including the x5 term). Give the general formula.
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