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47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)

47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)
Transcribed Image Text:47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)
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