Explanation Given: The function is f ( x , y , z ) = z ln ( y x ) Concept Used: ∇ f ( x 0 , y 0 , z 0 ) = f x ( x 0 , y 0 , z 0 ) i + f y ( x 0 , y 0 , z 0 ) j + f z ( x 0 , y 0 , z 0 ) The direction in which a function f ( x , y ) increases most rapidlyfrom point P 0 ( x 0 , y 0 , z 0 ) is given by ∇ f ( x 0 , y 0 , z 0 ) and magnitude of greatest rate of increase is ‖ ∇ f ( x 0 , y 0 , z 0 ) ‖ Calculation: In order to find the direction from P 0 ( 1 , e , − 1 ) in which the function f <

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 11.6, Problem 32PS

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To find the direction from P0(1,e,−1) in which the given function increases most rapidly also to compute the magnitude of the greatest rate of increase.

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Chapter 11.6, Problem 31PS

Chapter 11.6, Problem 33PS

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To find the direction from P 0 ( 1 , e , − 1 ) in which the given function increases most rapidly also to compute the magnitude of the greatest rate of increase.

Solution Summary: The author calculates the direction from P_0(1,e,-1) in which the given function increases most rapidly, and the magnitude of the greatest rate of increase.

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To find the direction from P0(1,e,−1) in which the given function increases most rapidly also to compute the magnitude of the greatest rate of increase.

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Chapter 11 Solutions