15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation sinh(x) = x + (x³/3!) when || < 0.5. (c) How close is the approximation sin(x) = x when || < 10-³? For which of these values of x is x < sin(x)?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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15. (a) Calculate e with an error of less than 10-6.
(b) Estimate the error in the approximation sinh(x) = x + (x³/3!) when |x| < 0.5.
(c) How close is the approximation sin(x) = x when |x| < 10-3? For which of these values of
x is x < sin(x)?
Transcribed Image Text:15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation sinh(x) = x + (x³/3!) when |x| < 0.5. (c) How close is the approximation sin(x) = x when |x| < 10-3? For which of these values of x is x < sin(x)?
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