Step 1:

The function is , .

Taylors theorem:

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

such that ,

Where

Here and .

Rewrite the function in polynomial form .

Differentiate with respect to on each side.

Determine by substituting corresponding values in .

Step 2:

The error cannot exceed 0.001 implies that

Taking fourth root on each side.

If , then  

So   and .

Therefore,

For , the value of is lies between

Solution:

The value of is lies between