Use the first five terms of the exponential series of eˣ and a calculator to approximate the value of e⁰.⁸ to the nearest hundredth.

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asked Jun 25, 2024 209k views

1 Answer

Unicorno Marley · Answer 1 · 2024-06-30T05:37:41+0000

To approximate the value of e⁰.⁸, use the first five terms of the exponential series of eˣ and evaluate them using a calculator.

To approximate the value of e⁰.⁸ using the first five terms of the exponential series of eˣ, we can use the formula:

eˣ = 1 + x + (x²/2!) + (x³/3!) + (x⁴/4!) + ...

Substituting x = 0.8 into the formula, we get:

e⁰.⁸ ≈ 1 + 0.8 + (0.8²/2!) + (0.8³/3!) + (0.8⁴/4!)

Using a calculator, we can evaluate each term and sum them up to approximate the value of e⁰.⁸ to the nearest hundredth.