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Sequences and Area

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See the attached document for proper formatting.

Find the centroid of the region bounded by the curves y = x + 2, y = x^2.

Set up the integral (do not integrate) of the area of between of the curves:

r = sin(2theta) and r = sin theta

(Hint. Sketch the curves, identify the region and use symmetry.)

Give an example of a divergent sequence {a_n}^infinity _n=1 and a convergent sequence {b_n}^infinity _n=1 so that the sequence {a_n + b_n}^infinity _n=1 is divergent.

Determine whether the given sequence is ultimately increasing, decreasing or neither. Explain. (Hint. Consider either the ratio a_n+1 / a_n, the difference a_n+1 - a_n or the function associated to the function if there is one.)

a. {n^2+1/n!}^infinity _n=1

b. {n / n^2 + 1}^infinity _n=1

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Solution Summary

This solution considers integrals, the area under a curve, and sequences. The solution is enclosed within an attached .zip file.

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