Math Problem Statement

Approximate cos(0.04) to five decimal-place accuracy using the Maclaurin series for cos(x) and check your work by comparing your answer to the function value produced directly by your calculating utility.

Solution

To solve this, we can approximate cos(0.04)\cos(0.04) using the Maclaurin series expansion for cos(x)\cos(x). The Maclaurin series for cos(x)\cos(x) is given by:

cos(x)=1x22!+x44!x66!+\cos(x) = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots

We will use enough terms to get an approximation accurate to five decimal places.

Let's calculate the approximation using x=0.04x = 0.04. I'll now compute that for you.Using the Maclaurin series for cos(0.04)\cos(0.04), the approximation up to four

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Math Problem Analysis

Mathematical Concepts

Calculus
Taylor/Maclaurin Series

Formulas

Maclaurin series for cos(x): cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...

Theorems

Maclaurin Series Expansion

Suitable Grade Level

University level (Calculus I/II)