Answer :
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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