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?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
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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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