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How to solve these two questions of calculus? 1. (2 marks) Aclass is discussing whether the following innite series converges or diverges. i loam) =2

How to solve these two questions of calculus?

1.

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(2 marks) Aclass is discussing whether the following innite series converges or diverges. i loam) \"=2 \"8/ 7 Zac, Mohamad, Joshua and Zahin believe the series converges and Mohammad, Snigdha, Dhruvik and Zachary believe the series diverges but everyone has a different reason. The reasons for both groups are listed below. Select all of the correct statement(s). The series converges by comparison, because for n large enough we have that 0 S 10g(n) and the series is divergent. \"8/7 \"14 _ \"14 712 10am) 1 and the series IS divergent. \"8/7 \"1/14 E2n1/14 0 1 divergent. _ _ log(n) 1 _ 0 1 The series converges by comparison, because for n large enough we have that 0 g ,for some (1 S 1 and the series 3 i m \"8/7 \"8/7(1 iris/7'9 convergent. (3 marks) _ Q 6 Consider the spiral given by the polar equation 71(0) 2 3e ,where 0 Z 0 . 3) Find the arc length of the spiral when 0 S 9 3 1r. :3 b) Find the total arc length of the spiral (if your answer is 00, just write infinity). em: l:a c) Find all values of g6 such that 71(0), 0 E R, and 72(9) = 11(0) - 396 , are the same spiral. You should find that there are innitely many possible values of :5 labeled by n E Z. Enter your answer in the box below. WE-B The answer to this question is a sequence {an }nZ . Write an expression for qn in the box below using Maple syntax. For example, for the expression 71.2 + 37m type n"2 + 3*Pi*n

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