Use the first five terms of the exponential series e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! +... to approximate e^3.9 to two decimal places.

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lopalr6egomartinGon lopalr6egomartinGon

24-12-2016
Mathematics

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Use the first five terms of the exponential series e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! +... to approximate e^3.9 to two decimal places.

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-12-26T06:45:01+01:00

nobillionaireNobley nobillionaireNobley

26-12-2016

e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + . . .
e^3.9 = 1 + 3.9 + (3.9)^2/2! + (3.9)^3/3! + (3.9)^4/4! = 1 + 3.9 + 15.21/2 + 59.319/6 + 231.3441/24 = 4.9 + 7.605 + 9.8865 + 9.6393 = 32.03

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