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x2 f(x) = e* = 1 + x + x3 x < 0 2! 3!' +

x2 f(x) = e* = 1 + x + x3 x < 0 2! 3!' +

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Question

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001.

x2 f(x) = e* = 1 + x + x3 x < 0 2! 3!' +
Transcribed Image Text:x2 f(x) = e* = 1 + x + x3 x < 0 2! 3!' +
Expert Solution
Step 1

Concept used:

Taylor expansion is used to calculate the approximate values of functions. 

Step 2

Error term for given polynomial:

E=ey x44!

According to the question:

E<0.001ey x44!<0.001

Multiply both sides by 4! :

eyx4<0.024

Take fourth root on both sides:

ey4x<0.3936

x<0.3936ey4

 

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