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Consider the region bounded by the graphs of y = ax", y = ab°, and x = 0. (b > 1. See Figure.) (a) Find the ratio R,(n) of the area of the region to the area of the circumscribed rectangle. R,(n) = (b) Find the limit shown below. lim R,(n) Find the limit of the area of the circumscribed rectangle as n approaches infinity. (c) Find the volume of the solid of revolution formed by revolving the region about the y-axis. z(a)(b)"+2 Find the ratio R,(n) of this volume to the volume of the circumscribed right circular cylinder. Ry(n) = (d) Find the limit shown below. lim R,(n) 1 Find the limit of the volume of the circumscribed cylinder as n approaches infinity. 00 ax" (0 s x s b) as n→ «. (e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y= O As n-, the graph approaches the line y = a. O As n-, the graph approaches the line x = b. • As n-, the graph approaches the line y = 0. O As n-, the graph approaches the line x = 0. O As n-, the graph approaches the line x = a. O As n-, the graph approaches the line y = b.

Consider the region bounded by the graphs of y = ax", y = ab°, and x = 0. (b > 1. See Figure.) (a) Find the ratio R,(n) of the area of the region to the area of the circumscribed rectangle. R,(n) = (b) Find the limit shown below. lim R,(n) Find the limit of the area of the circumscribed rectangle as n approaches infinity. (c) Find the volume of the solid of revolution formed by revolving the region about the y-axis. z(a)(b)"+2 Find the ratio R,(n) of this volume to the volume of the circumscribed right circular cylinder. Ry(n) = (d) Find the limit shown below. lim R,(n) 1 Find the limit of the volume of the circumscribed cylinder as n approaches infinity. 00 ax" (0 s x s b) as n→ «. (e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y= O As n-, the graph approaches the line y = a. O As n-, the graph approaches the line x = b. • As n-, the graph approaches the line y = 0. O As n-, the graph approaches the line x = 0. O As n-, the graph approaches the line x = a. O As n-, the graph approaches the line y = b.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I only need e and c i know the rest are correct. but I know E and C might be incorrect

Consider the region bounded by the graphs of y = ax", y = ab", and x = 0. (b > 1. See Figure.) ab" y=ax" (a) Find the ratio R, (n) of the area of the region to the area of the circumscribed rectangle. n R (n) = n +1 (b) Find the limit shown below. lim R,(n) n → 00 1 Find the limit of the area of the circumscribed rectangle as n approaches infinity. (c) Find the volume of the solid of revolution formed by revolving the region about the y-axis. a(a)(b)"+2( n n+2 Find the ratio R,(n) of this volume to the volume of the circumscribed right circular cylinder. n R2(n) = n + 2 (d) Find the limit shown below. lim R2(n) n → 00 1 Find the limit of the volume of the circumscribed cylinder as n approaches infinity. (e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y = ax" (0 < x < b) as n → o. O As n → 0, the graph approaches the line y = a. As n → o, the graph approaches the line x = b. As n → o, the graph approaches the line y = 0. As n → o, the graph approaches the line x = 0. As n → o, the graph approaches the line x = a. O As n → o, the graph approaches the line y = b.
Transcribed Image Text:Consider the region bounded by the graphs of y = ax", y = ab", and x = 0. (b > 1. See Figure.) ab" y=ax" (a) Find the ratio R, (n) of the area of the region to the area of the circumscribed rectangle. n R (n) = n +1 (b) Find the limit shown below. lim R,(n) n → 00 1 Find the limit of the area of the circumscribed rectangle as n approaches infinity. (c) Find the volume of the solid of revolution formed by revolving the region about the y-axis. a(a)(b)"+2( n n+2 Find the ratio R,(n) of this volume to the volume of the circumscribed right circular cylinder. n R2(n) = n + 2 (d) Find the limit shown below. lim R2(n) n → 00 1 Find the limit of the volume of the circumscribed cylinder as n approaches infinity. (e) Use the results of parts (b) and (d) to make a conjecture about the shape of the graph of y = ax" (0 < x < b) as n → o. O As n → 0, the graph approaches the line y = a. As n → o, the graph approaches the line x = b. As n → o, the graph approaches the line y = 0. As n → o, the graph approaches the line x = 0. As n → o, the graph approaches the line x = a. O As n → o, the graph approaches the line y = b.
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