Determine if each converges or diverges and...

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AMS 161-Final Exam-Spring 2015 NAME: ° 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) 1 X n =1 ( e n ) 2 b) 1 X n =1 n ! 5 n 1
c) 1 X n =2 1 n ln n d) 1 X n =1 ( ° 1) n p 3 n 2
2. Use the trapezoid rule with 3 subintervals to estimate the area between dy dx = 2 ° x and the x axis from x = ± 3 to x = 3 . Now use this value to sketch y = f ( x ) if f ( ± 3) = 4 3
3. If the half-life of a radioactive substance is 20 years, how long will it take to decay by 80% assuming the rate of change of this substance is directly proportional to the amount present? Derive any formulas

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