Step 1:

The function .

From the Taylor polynomial is fifth degree polynomial.

Formula:

in .

Error

The error cannot exceed 0.001.

Solution:

.

Second way: in Q&A.

Step 1:

The function .

Taylors theorem:

If a function is differentiable through order in an interval containing , then for each in ,there exist between and such that , ,

where error .

Here and .

From the Taylor polynomial it is fifth degree polynomial.

Determine by substituting corresponding values in .

in .

Step 2:

Error

The error cannot exceed 0.001 implies that .

Solution:

.