Can you answer A, B- i, ii, and C please?

Problem 2: [60 pts] Short Answer Directions: Answer the questions below and explain your responses. Correct responses with little to no reasoning or explanations that rely on technology will earn no credit. Correct responses with incomplete explanations will not receive full credit. A. [20 pts] Evaluate / sec3(x) tan(x) dx. B. [20 pts] For this problem, you may use the fact that the Taylor series for In(1 + 2.?) is (-1)*+1 . 2k 2- 2k k= 1 k i. [10 pts] Approximate In(1.8) by using the fourth order Taylor polynomial for In(1 + 2r?) centered at x = 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. C. [20 pts] Morgan, Avery, and Taylor are asked to evaluate the limit lim why - yz (x,y)=(2,4) 24 - 12 . Morgan writes lim ry- yz (x,y)=(2,4) a4 - y2 . Based on this, Morgan concludes that the limit does not exist. . Avery notes that along a = 0, czy - yz 0 - y2 = 1 and that along y = 0. "-y - y? 0-0 24 - 12 0 - 32 x4 - y2 x4 - 0 = 0. Avery concludes that the limit does not exist. . Taylor notes that along y = mr, Try - y2 mrs - m2x2 mx - m omx - m? 24 - yz x4 - m2x2 x2 - m2 , and as r -+ 0, x2 - m? -+ 1. Taylor concludes that the limit exists and is equal to 1. Determine which students, if any, provided a correct response. If a student did not provide a correct response, make sure to explain what error (or errors) they made. If none of the students are correct, calculate the limit correctly, or explain why it does not exist