please solve both parts, thank you.

B. (20 pts] For this problem, you may use the fact that the Taylor series for In(1 + 2.?) is (-1)*+1. 24 k = 1 i. [10 pts] Approximate In(1.8) by using the fourth order Taylor polynomial for In(1 + 2x?) centered at a = 0. ii. [10 pts] Explain whether you think the 24-th order Taylor polynomial would give a better or worse approximation for In(1.8) than the fourth order polynomial. Your explanation should reference facts about Taylor series; you may not simply calculate In(1.8) and both approximations