Ignore the top, cut off question Certainly! Below is the transcription of the image, formatted for an educational website.---### Mathematical Problems on Surface Tangents and Linearization#### 5. Tangent to the SurfaceConsider 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 EquationA 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 FunctionFind 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,

Name: Ignore the top, cut off question Certainly! Below is the transcription
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Description: Ignore the top, cut off question Certainly! Below is the transcription of the image, formatted for an educational website.---### Mathematical Problems on Surface Tangents and Linearization#### 5. Tangent to the SurfaceConsider the surface given by th

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Answered: 5. On the surface z-3x^2+2y^2 (an…

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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

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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1+y Find the tangent plane to the surface z = at the point P (-2, -4, 3). 1+x Type in the equation of the plane with the accuracy of at least 2 significant figures for each coefficient. z = ( )x + ( )y + (
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y= 2x^3-1 y=x^2-2x
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a circle is tangent to the line 2x-y+1=0 at the point (2,5) and the center is on the line x+y=9. find the equation of the circle.
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