Maclaurin-theorem

Question

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.

sin (0.3)

Answer 1

Step 1:

The expression is .

Consider, the function .

Error cannot exceed .

Formula for error in Taylor series is :

, Where any number between and .

The derivative of  function is less than or equal to 1, for all values of .

, Where any number between and .

Substitute in .

Substitute  in .

.

Comments

Contd...

Step 2:

Find value by trial and error method.

Take and substitute in .

, the statement is false.

Take and substitute in .

, the statement is false.

Take and substitute in .

, statement is false.

Take and substitute in .

, the statement is true.

So, degree of the Maclaurin polynomial is .

Solution:

Degree of the Maclaurin polynomial is .