5. Provide a 3rd order Taylor polynomial for f(x) = x1/3 when a = 1. Use the polynomial to approximate the cube root of 2. 6. Approximate f(x) = ell around 0 using a 5th order Taylor polynomial. Use Taylor polynomial to approximate e 25. Provide an upper bound on the absolute error of this approximation. 7. (Bonus) The error term for a Taylor polynomial of degree n for f near x = a is given by R I = 14m3 (x a)n+1) when c is between r and a. What degree of a Taylor polynomial is needed to represent a reasonable approximation of sin(a) on the interval of (0,2) based on the maximum precision that is allowed with a IEEE 754 single precision number? (Hint: Achieve an error bound that is less than 10-7.]