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√₁-²²2 x² y² and the point P(-√2,0) on the level curve f(x,y) = Compute the slope of the line tangent to 4 16 1 √2 Consider the ellipsoid f(x,y) = 1- the level curve at P and verify that the tangent line is orthogonal to the gradient at that point. What is the slope of the tangent line to the level curve at P(-√2,0) ? Select the correct choice below and, if necessary, fill in the answer box in your choice. OA. The slope at P (-√√2,0) is. OB. The slope at P (-√√2,0) is undefined, so the tangent line is vertical. How do you know the gradient and tangent line are orthogonal? Select the correct choice below and fill in the answer boxes in your choice. O A. The slope of the tangent line, m, can be used to write a vector in the direction of the tangent line, (1,m). The dot product of this vector and the gradient is 0, so they are orthogonal. OB. The tangent line slope is undefined, so it is a vertical line. The gradient is horizontal, so it is orthogonal to the tangent line.

√₁-²²2 x² y² and the point P(-√2,0) on the level curve f(x,y) = Compute the slope of the line tangent to 4 16 1 √2 Consider the ellipsoid f(x,y) = 1- the level curve at P and verify that the tangent line is orthogonal to the gradient at that point. What is the slope of the tangent line to the level curve at P(-√2,0) ? Select the correct choice below and, if necessary, fill in the answer box in your choice. OA. The slope at P (-√√2,0) is. OB. The slope at P (-√√2,0) is undefined, so the tangent line is vertical. How do you know the gradient and tangent line are orthogonal? Select the correct choice below and fill in the answer boxes in your choice. O A. The slope of the tangent line, m, can be used to write a vector in the direction of the tangent line, (1,m). The dot product of this vector and the gradient is 0, so they are orthogonal. OB. The tangent line slope is undefined, so it is a vertical line. The gradient is horizontal, so it is orthogonal to the tangent line.

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 91E
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Consider the ellipsoid f(x,y) = 1 2 X 2 1 and the point P ( - √2,0) on the level curve f(x,y) = √2 Compute the slope of the line tangent to 16 4 the level curve at P and verify that the tangent line is orthogonal to the gradient at that point. What is the slope of the tangent line to the level curve at P(- √2,0) ? Select the correct choice below and, if necessary, fill in the answer box in your choice. A. The slope at P (-√√2,0) is OB. The slope at P (-√√2,0) is undefined, so the tangent line is vertical. How do you know the gradient and tangent line are orthogonal? Select the correct choice below and fill in the answer boxes in your choice. O A. The slope of the tangent line, m, can be used to write a vector in the direction of the tangent line, (1,m). The dot product of this vector and the gradient is 0, so they are orthogonal. OB. The tangent line slope is undefined, so it is a vertical line. The gradient is horizontal, so it is orthogonal to the tangent line.
Transcribed Image Text:Consider the ellipsoid f(x,y) = 1 2 X 2 1 and the point P ( - √2,0) on the level curve f(x,y) = √2 Compute the slope of the line tangent to 16 4 the level curve at P and verify that the tangent line is orthogonal to the gradient at that point. What is the slope of the tangent line to the level curve at P(- √2,0) ? Select the correct choice below and, if necessary, fill in the answer box in your choice. A. The slope at P (-√√2,0) is OB. The slope at P (-√√2,0) is undefined, so the tangent line is vertical. How do you know the gradient and tangent line are orthogonal? Select the correct choice below and fill in the answer boxes in your choice. O A. The slope of the tangent line, m, can be used to write a vector in the direction of the tangent line, (1,m). The dot product of this vector and the gradient is 0, so they are orthogonal. OB. The tangent line slope is undefined, so it is a vertical line. The gradient is horizontal, so it is orthogonal to the tangent line.
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