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5. On the surface z-3x^2+2y^2 (an elliptic paraboloid), (x,y) changes from (1,1) to (0.99,1.02). Use the differential dz to approximate the change Az in the value of z

5. On the surface z-3x^2+2y^2 (an elliptic paraboloid), (x,y) changes from (1,1) to (0.99,1.02). Use the differential dz to approximate the change Az in the value of z

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Certainly! Below is the transcription of the image, formatted for an educational website. --- ### Mathematical Problems on Surface Tangents and Linearization #### 5. Tangent to the Surface Consider the surface given by the equation \( z = x^2 + y^2 \), which represents an elliptic paraboloid. We use the differential \( dz \) to approximate the change \( \Delta z \) in the value of \( z \), as the point changes from (1,1) to (1.01, 0.99). Select one: - A. \( \Delta z \approx 0.02 \) - B. \( \Delta z \approx 0.018 \) - C. \( \Delta z \approx 0.022 \) - D. \( \Delta z \approx 0.015 \) - E. \( \Delta z \approx 0.019 \) *Written calculations indicate use of partial derivatives to compute the differential \( dz \).* #### 6. Tangent Plane Equation A function \( z = f(x, y) \) has a differential. Find an equation for the tangent plane to the graph of \( f(x, y) \) at the point (1, 2, 5). Select one: - A. \( z = 2x + 3y - 1 \) - B. \( z = 2x + 3y + 1 \) - C. \( z = 3x + 3y - 5 \) - D. \( z = 8x + 2y \) - E. \( z = 3x + 2y + 7 \) *The handwritten notes show calculations of partial derivatives and substitution of coordinates to find the tangent plane.* #### 7. Linearization of a Function Find the linearization \( L(x, y) \) of the function \( f(x, y) = xe^{xy} \) at the point (2,0), and use it to approximate the value of \( f(2.1, -0.2) \). Select one: - A. \( f(2.1, -0.2) \approx 2 \) - B. \( f(2.1, -0.2) \approx 0.9 \) *Calculations show derivations for \( L(x,
Transcribed Image Text:Certainly! Below is the transcription of the image, formatted for an educational website. --- ### Mathematical Problems on Surface Tangents and Linearization #### 5. Tangent to the Surface Consider the surface given by the equation \( z = x^2 + y^2 \), which represents an elliptic paraboloid. We use the differential \( dz \) to approximate the change \( \Delta z \) in the value of \( z \), as the point changes from (1,1) to (1.01, 0.99). Select one: - A. \( \Delta z \approx 0.02 \) - B. \( \Delta z \approx 0.018 \) - C. \( \Delta z \approx 0.022 \) - D. \( \Delta z \approx 0.015 \) - E. \( \Delta z \approx 0.019 \) *Written calculations indicate use of partial derivatives to compute the differential \( dz \).* #### 6. Tangent Plane Equation A function \( z = f(x, y) \) has a differential. Find an equation for the tangent plane to the graph of \( f(x, y) \) at the point (1, 2, 5). Select one: - A. \( z = 2x + 3y - 1 \) - B. \( z = 2x + 3y + 1 \) - C. \( z = 3x + 3y - 5 \) - D. \( z = 8x + 2y \) - E. \( z = 3x + 2y + 7 \) *The handwritten notes show calculations of partial derivatives and substitution of coordinates to find the tangent plane.* #### 7. Linearization of a Function Find the linearization \( L(x, y) \) of the function \( f(x, y) = xe^{xy} \) at the point (2,0), and use it to approximate the value of \( f(2.1, -0.2) \). Select one: - A. \( f(2.1, -0.2) \approx 2 \) - B. \( f(2.1, -0.2) \approx 0.9 \) *Calculations show derivations for \( L(x,
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