Explanation Given: Key concepts applied: We need to draw triangles from the figure and label the distances as shown in the figure below: By repeated application of the Pythagorean Theorem, We find ( d + R ) 2 = k 2 + R 2 → 1 s t E q u a t i o n (Applying Pythagorean Theorem to Bigger Triangle) k 2 = ( d + h ) 2 + x 2 → 2 n d E q u a t i o n (Applying Pythagorean Theorem to Medium Triangle) R 2 = x 2 + ( R − h ) 2 → 3 r d E q u a t i o n (Applying Pythagorean Theorem to Smaller Triangle) Substituting the 2 nd and 3 rd equation in 1 st equation we get… ( d + R ) 2 = ( d + h ) 2 + x 2 + x 2 + ( R − h ) 2 → 4 s t E q u a t i o n Formula used: Pythagorean Theorem: a 2 + b 2 = c 2 (where a and b are legs of Right Triangle and c is Hypotenuse) Algebraic Identities: ( m + n ) 2 = m 2 + n 2 + 2 m n ( m − n ) 2 = m 2 + n 2 − 2 m n Calculation: Solving for h yields… ( d + R ) 2 = ( d + h ) 2 + x 2 + x 2 + ( R − h ) 2 d 2 + R 2 + 2 d R = d 2 + 2 d h + h 2 + 2 x 2 + R 2 + h 2 − 2 R h G e t t i n g a l l t h e t e r m s i n o n e s i d e o f t h e e q u a t i o n , w e g e t d 2 + R 2 + 2 d R − ( d 2 + 2 d h + h 2 + 2 x 2 + R 2 + h 2 − 2 R h ) = 0 D i s t r i b u t i n g t h e n e g a t i v e d 2 + R 2 + 2 d R − d 2 − 2 d h − h 2 − 2 x 2 − R 2 − h 2 + 2 R h = 0 C o m b i n i n g l i k e t e r m s d 2 + R 2 + 2 d R − d 2 − 2 d h − h 2 − 2 x 2 − R 2 − h 2 + 2 R h = 0 2 d R + 2 R h − 2 d h − 2 h 2 − 2 x 2 = 0 F r o m 3 r d E q u a t i o n ,

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 9.2, Problem 63E

To determine

The limit of the observed $A r e a A = 2 π d \cdot (\frac{R^{2}}{d + R})$ when $d \to \infty$

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Chapter 9.2, Problem 62E

Chapter 9.2, Problem 64E

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Chapter 9 Solutions

CALCULUS (CLOTH)

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.2 - Prob. 1PQ Ch. 9.2 - Prob. 2PQ Ch. 9.2 - Prob. 3PQ Ch. 9.2 - Prob. 4PQ Ch. 9.2 - Prob. 5PQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - Prob. 49E Ch. 9.2 - Prob. 50E Ch. 9.2 - Prob. 51E Ch. 9.2 - Prob. 52E Ch. 9.2 - Prob. 53E Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - Prob. 60E Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - Prob. 63E Ch. 9.2 - Prob. 64E Ch. 9.2 - Prob. 65E Ch. 9.3 - Prob. 1PQ Ch. 9.3 - Prob. 2PQ Ch. 9.3 - Prob. 3PQ Ch. 9.3 - Prob. 4PQ Ch. 9.3 - Prob. 5PQ Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.4 - Prob. 1PQ Ch. 9.4 - Prob. 2PQ Ch. 9.4 - Prob. 3PQ Ch. 9.4 - Prob. 4PQ Ch. 9.4 - Prob. 5PQ Ch. 9.4 - Prob. 6PQ Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.4 - Prob. 21E Ch. 9.4 - Prob. 22E Ch. 9.4 - Prob. 23E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 27E Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 31E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 35E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Prob. 43E Ch. 9.4 - Prob. 44E Ch. 9.4 - Prob. 45E Ch. 9.4 - Prob. 46E Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Prob. 50E Ch. 9.4 - Prob. 51E Ch. 9 - Prob. 1CRE Ch. 9 - Prob. 2CRE Ch. 9 - Prob. 3CRE Ch. 9 - Prob. 4CRE Ch. 9 - Prob. 5CRE Ch. 9 - Prob. 6CRE Ch. 9 - Prob. 7CRE Ch. 9 - Prob. 8CRE Ch. 9 - Prob. 9CRE Ch. 9 - Prob. 10CRE Ch. 9 - Prob. 11CRE Ch. 9 - Prob. 12CRE Ch. 9 - Prob. 13CRE Ch. 9 - Prob. 14CRE Ch. 9 - Prob. 15CRE Ch. 9 - Prob. 16CRE Ch. 9 - Prob. 17CRE Ch. 9 - Prob. 18CRE Ch. 9 - Prob. 19CRE Ch. 9 - Prob. 20CRE Ch. 9 - Prob. 21CRE Ch. 9 - Prob. 22CRE Ch. 9 - Prob. 23CRE Ch. 9 - Prob. 24CRE Ch. 9 - Prob. 25CRE Ch. 9 - Prob. 26CRE Ch. 9 - Prob. 27CRE Ch. 9 - Prob. 28CRE

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The limit of the observed A r e a A = 2 π d ⋅ ( R 2 d + R ) when d → ∞

Solution Summary: The author explains how to determine the limit of the observed A r e a when d .

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The limit of the observed $A r e a A = 2 π d \cdot (\frac{R^{2}}{d + R})$ when $d \to \infty$

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Chapter 9 Solutions

The limit of the observed A r e a A = 2 π d ⋅ ( R 2 d + R ) when d → ∞

Solution Summary: The author explains how to determine the limit of the observed A r e a when d .

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The limit of the observed Area A=2πd⋅(R2d+R) when d→∞

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Chapter 9 Solutions

The limit of the observed $A r e a A = 2 π d \cdot (\frac{R^{2}}{d + R})$ when $d \to \infty$