hmwk5 - Math 215 Homework Set 5: 15.6 15.7 Fall 2007 Most...

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Unformatted text preview: Math 215 Homework Set 5: 15.6 15.7 Fall 2007 Most of the following problems are modiFed versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 15.6a. Use the table for wave heights in Problem 4 of 15.3 of Stewarts Multivariable Calculus to estimate the value of D u f (30 , 20) , where u = ( i + j ) / 2 . 15.6b. ind the directional derivative of f ( x, y, z ) = x 2 + 3 y 2- 2 z 2 at the point (3 , 5 , 4) in the direction of the origin. 15.6c. Show that a differentiable function f decreases fastest at a point P in the direction opposite the gradient vector at P . In which direction is the function f ( x, y, z ) = x 2 + 3 y 2- 2 z 2 decreasing the fastest at the point (3 , 5 , 4) ? 15.6d. After copying the Fgure from problem 36 of 15.6 in Stewarts Multivariable Calculus , please do the problem. 15.6e. After copying the Fgure from problem 38 of 15.6 in Stewarts Multivariable Calculus , please do the problem.the problem....
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