Question

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.

Answer 1

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

Step-by-step explanation:

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.