Approximate the specified function value as indicated and...

Approximate the specified function value as indicated and check your work by comparing your answer to the function value produced directly by your calculating utility.
Approximate cosh 0.1 to three decimal-place accuracy using the Maclaurin series for $\cosh$ x .

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Key Concepts

Hyperbolic Cosine Function

The hyperbolic cosine function, denoted as cosh(x), is defined as (e^x + e^(-x))/2. It is an even function and its properties, including its series expansion, are useful in various fields such as engineering, physics, and applied mathematics. Its Maclaurin series expansion contains only even-powered terms, which reflects its even symmetry.

Maclaurin Series

A Maclaurin series is a specific form of a Taylor series expanded about zero. It represents functions as infinite sums of powers of x with coefficients determined by the function's derivatives at zero. This tool is crucial in approximating functions by truncating the series after a finite number of terms, which can simplify complex calculations.

Series Approximation and Error Estimation

Series approximation involves using a finite sum of terms from an infinite series to estimate the value of a function. Error estimation is the process of determining how many terms are needed to achieve a desired level of accuracy, such as three decimal places. This concept helps in balancing computational efficiency with the precision of the approximation.

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