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AMS 161-Final Exam-Spring 2015NAME:°Question 1 is worth 16 points. Questions 2 -7 are 14 points each SHOW ALL WORK!1. Determine if each converges or diverges and justify:a)1Xn=1(en)2b)1Xn=1n!5n1
2. Use the trapezoid rule with 3 subintervals to estimate the area betweendydx= 2°xand the x axis fromx=±3tox= 3. Now use this value to sketchy=f(x)iff(±3) = 43
3. If the half-life of a radioactive substance is 20 years, how long will it take to decay by 80% assumingthe rate of change of this substance is directly proportional to the amount present? Derive any formulas