6. Approximate f(x) = et 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 r = a is given by R I = 14(n+1)! Amt) (x - a)n+1 when e is between x and a. What degree of a Taylor polynomial is needed to represent a reasonable approximation of sin(x) 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.]