Consider the region bounded by the graphs of y = ax n , y = ab n
Question:
Consider the region bounded by the graphs of y = axn, y = abn, and x = 0, as shown in the figure.
(a) Find the ratio R1(n) of the area of the region to the area of the circumscribed rectangle.(b) Find lim n ∞ R1(n) and compare the result with the area of the circumscribed rectangle.(c) Find the volume of the solid of revolution formed by revolving the region about the y-axis. Find the ratio R2(n) of this volume to the volume of the circumscribed right circular cylinder.(d) Find lim n ∞ R2(n) and compare the result with the volume of the circumscribed cylinder.(e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y = axn, 0 ≤ x ≤ b, as n ∞.
Step by Step Answer:
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards