(10.07 mc) given what degree maclaurin polynomial is required so that the error in the approximation is less than 0.001?

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06-12-2022
Mathematics

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(10.07 mc) given what degree maclaurin polynomial is required so that the error in the approximation is less than 0.001?

Sagot :

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ShubhamSrivastava ShubhamSrivastava · Answer 1 · 2022-12-14T08:44:10-05:00

n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

Given that,

The expression is

e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

We have to find what degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

We know that,

What is the polynomial?

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

√e=1.64872

Pₙ( x)= e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

P₂=1+0.5+0.5²/2!=1.625

P₃= P₂+0.5³/3!=1.6458

P₄= P₃+0.5⁴/4!=1.648404

√e - P₄ = -0.0003158

Therefore, n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

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Sagot :

What is the polynomial?

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