Problem 26E

Approximations with Taylor polynomials

a. Use the given Taylor polynomial p2 to approximate the given quantity.

b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Approximate using and p2(x) = 1 − 3x + 6x2.

Solution 26E

Step 1:

In this problem , we have to find out the approximation value by using taylor's polynomial.

The Taylor polynomial of degree n centered at x = a approximating the function f(x) is;

= f(a) +(x-a) +

=