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 and 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 ≤

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

< e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! )

where m =

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

step-by-step explanation:

no of data

divide by no of mode