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Naddika [18.5K]
3 years ago
14

Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper a

nd pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Mathematics
1 answer:
UNO [17]3 years ago
5 0

Answer:

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

e^{0.4 < e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! ) | x-a |^{N+1

where m = | f^{N+1 }(x) |

so we have

| Error |  ≤ ( 3 / ( 3 + 1 )! ) | -0.4 |⁴

| Error |  ≤ ( 3 / 4! ) | -0.4 |⁴

| Error |  ≤ ( 3 / 24 ) | -0.4 |⁴

| Error |  ≤ ( 0.125 ) | -0.0256 |

| Error |  ≤ ( 0.125 ) 0.0256

| Error |  ≤ 0.0032

Therefore, upper bound for the error, | Error |  ≤ 0.0032

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