Determine if each converges or diverges and...

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AMS 161-Practice Final Exam-Fall 2018 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 (2 n )! 2 n !2 n b) 1 X n =1 (5 + 1 n 99 ) 1
c) 1 X n =2 ln n n d) 1 X n =1 26 n ° 27 n 100 n 2
2. Shetch F ( x ) = R x ° 1 p t 3 + 1 dt using the fundamental theorem of calculus. Accurate y values are not required here. 3
3. If the half-life of a radioactive substance is 10 years, how long will it take to decay by 30% assuming the rate of change of this substance is directly proportional to the amount present? Derive any formulas you use by solving a di/erential equation!

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