Polar Coordinate System Calculus Questions Hello everyone, I have the Calculus questions, please solve each question in details. 1. Determine whether addin

Polar Coordinate System Calculus Questions Hello everyone, I have the Calculus questions, please solve each question in details. 1. Determine whether adding the first 100 terms of the series ?
(?1)??
gives you either an
??
overestimate or underestimate of the sum of the series.
2. True or False: If the infinite series ? ???? and ? ???? both converge, then the
series ? ???? ???? converges also. If false, explain why or provide a counterexample.
3. The following argument concludes that 0 = 1, which is false. Describe the error in the
argument.
0 = 0 + 0 + 0 + …
0 = (1 – 1) + (1 – 1) + (1 – 1) +…
0 = 1 + ( – 1 + 1) + (- 1 + 1) + ( – 1 + 1) + …
0 = 1 (?? ! !)
3. True or false: If (r1, ?1) and (r2, ?2) represent the same point on the polar
coordinate system, then ?1=?2. If false, explain why or provide a counterexample.
5. True or false: The polar equations r = sin (2?), r = – sin (2?), and r = sin (-2?) all have
the same graph. If false, explain why or provide a counterexample.

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