Determine the range of x over which the Taylor expansion of ln(1 + x) about x = 1.5 will converge. Note that this result was stated but not proved in Example 5.19.

Example 5.19

Develop a third-order polynomial that approximates ln(1 + x) close to x = 1.5. Use this expression to approximate the function at x = 1.3 and 1.6.