Explanation Given: The function f ( x ) = e x and | e − T n ( 1 ) | < 10 − 8 , where T n ( x ) is the Maclaurin polynomial for f ( x ) = e x . Formula used: The maximum possible error in approximating the Taylor polynomial T n ( x ) at x = a is given as | E n ( x ) | = | f ( n + 1 ) ( a ) ( n + 1 ) ! ( x − a ) n + 1 | Calculation: The maximum possible value of the error | e x − T n ( x ) | can be given as | e x − T n ( x ) | = | E n ( x ) | = | f ( n + 1 ) ( 0 ) ( n + 1 ) ! ( x − 0 ) n + 1 | = | f ( n + 1 ) ( 0 ) ( n + 1 ) ! x n + 1 | Recall f ( n + 1 ) ( x ) = e x

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Author: Rogawski

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Chapter 11, Problem 123CRE

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The value of n such that |e−Tn(1)|<10−8 if Tn(x) is the Maclaurin polynomial for f(x)=ex .

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Chapter 11, Problem 122CRE

Chapter 11, Problem 124CRE

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Chapter 11 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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The value of n such that | e − T n ( 1 ) | < 10 − 8 if T n ( x ) is the Maclaurin polynomial for f ( x ) = e x .

Solution Summary: The author calculates the maximum possible error in approximating the Taylor polynomial T_n(x).

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The value of n such that |e−Tn(1)|<10−8 if Tn(x) is the Maclaurin polynomial for f(x)=ex .

Want to see the full answer?

Chapter 11 Solutions

The value of n such that | e − T n ( 1 ) | &lt; 10 − 8 if T n ( x ) is the Maclaurin polynomial for f ( x ) = e x .

Solution Summary: The author calculates the maximum possible error in approximating the Taylor polynomial T_n(x).

Videos

The value of n such that |e−Tn(1)|<10−8 if Tn(x) is the Maclaurin polynomial for f(x)=ex .

Want to see the full answer?

Chapter 11 Solutions

The value of n such that | e − T n ( 1 ) | < 10 − 8 if T n ( x ) is the Maclaurin polynomial for f ( x ) = e x .