Question

Consider the region bounded by the graphs of y # ax', y abn, :0.(b>1. See Figure.) and x (a) Find the ratio R(n) of the area of the region to the area of the circumscribed rectangle R1(n)-| n + 1 (b) Find the limit shown below. lim Ri(n) Find the limit of the area of the circumscribed rectangle as n approaches in (e) Find the volume of the solid of revolution formed by revolving the region about the yraxis. rab2 2 n+ 2 Find the ratio R2(n) of this volume to the volume of the circumscribed right circular cylinder. lim R2(n) (e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y-ax (o sxs b) as n +o. O Asnoo, the graph approaches the line y b As n +oo, the graph approaches the line x0.

Answer 1

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