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Cartesian Coordinates, Convergence and Divergence

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1. Find the equation of the tangent line in Cartesian coordinates of the curve given in polor coordinates by

r = 3 - 2 cos Ø, at Ø= (π / 3)

2.Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

a) ∑[∞/n=1] (3/ 2^n)

b) ∑[∞/n=2] (1 / n ln n)

c) ∑[∞/n=0] (((3n^2) + n +1) / (n^4+1))

d) ∑[∞/n=1] ((n+1)/(2n+3))

e) ∑[∞/n=1] ((n!) / (2^n) (n^2))

f) ∑[∞/n=1] (((-1)^n) /( n^(1/2)))

3. Find the open interval of convergence and test the endpoints for absolute and conditional convergence.

a) ∑[∞/ n=1] ((x+1)^n) / ((3^n)(n))

b) ∑[∞/n=1] ((x-4)^(n+1)) / ((n+3)^2)

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Cartesian Coordinates, Convergence and Divergence are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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