# Evaluating ln(x + sqrt[1+x2]) - sin(x) at x=.001

• psyklon
In summary, the problem requires evaluating a function at a given point, specifically ln(x + sqrt[1+x2] ) - sin(x) at x = .001. The equations used for this solution are the power series expansions for sin(x) and ln(1 + x). Since x is small, the approximation of sin(x) as just x can be used, and the same can be done for the other functions.
psyklon

## Homework Statement

The problem I'm attempting to solve asks you to evaluate the function at a given point. In this case:

ln(x + sqrt[1+x2] ) - sin(x)
@ x = .001

## Homework Equations

sin(x) = x - (x3/3!) + (x5/5!) - (x7/7!) + ...
AND
ln(1 + x) = x - (x2/2) + (x3/3) - (x4/4) + ...

## The Attempt at a Solution

I know I'm supposed to substitute in the power series expansions, but I'm not sure how to begin modifying the second expansion to suit my needs in solving the problem. Can anyone point me in the right direction?

Since x is small, you can approximate sin(x) as just x, you can do the same with the other functions.

## What is the function being evaluated?

The function being evaluated is ln(x + sqrt[1+x^2]) - sin(x).

## What is the value of x being used?

The value of x being used is 0.001.

## Why is this function being evaluated at x = 0.001?

This value of x is commonly used in scientific and mathematical calculations as it is a very small number close to 0.

## What is the purpose of evaluating this function?

The purpose of evaluating this function is to gain a better understanding of its behavior and properties, which can then be applied in various scientific and mathematical contexts.

## What is the result of this evaluation?

The result of evaluating ln(x + sqrt[1+x^2]) - sin(x) at x = 0.001 is approximately 0.00049998.

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