Please give as much detail as possible because I am trying to learn as I go through the answer. Complete each of the following.(a) Find an equation of the plane tangent to the surface $ f(x, y) = xy^2 - 5x $ at the point $ (1, 2, -1) $.(b) Find the linearization $ L(x, y) $ of the function in part (a) near the given point. Use this function to approximate the value of $ f(0.99, 2.02) $ by hand.(c) Suppose that $ F : \mathbb{R}^3 \to \mathbb{R} $ is a function such that the level surface $ F(x, y, z) = -1 $ is the unit sphere of $ \mathbb{R}^3 $ centered at the origin. Identify the function $ F(x, y, z) $ and find both the tangent plane to this level surface at the point $ (0, -1, 0) $ and the parametric equations of the line normal to this surface through the given point.

step:-1 Let surface f(x,y) and z=f(x,y) then equation of tangent plane at (a, b ,c) is (z-c)=fx(a,…

(a) Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the point (1, 2, – 1). | (b) Find the linearization L(x, y) of the function in part (a) near the given point. Use this function to approximate the value of f(0.99, 2.02) by hand.

(a) Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the point (1, 2, – 1). | (b) Find the linearization L(x, y) of the function in part (a) near the given point. Use this function to approximate the value of f(0.99, 2.02) by hand.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please give as much detail as possible because I am trying to learn as I go through the answer.

Complete each of the following.

(a) Find an equation of the plane tangent to the surface $ f(x, y) = xy^2 - 5x $ at the point $ (1, 2, -1) $.

(b) Find the linearization $ L(x, y) $ of the function in part (a) near the given point. Use this function to approximate the value of $ f(0.99, 2.02) $ by hand.

(c) Suppose that $ F : \mathbb{R}^3 \to \mathbb{R} $ is a function such that the level surface $ F(x, y, z) = -1 $ is the unit sphere of $ \mathbb{R}^3 $ centered at the origin. Identify the function $ F(x, y, z) $ and find both the tangent plane to this level surface at the point $ (0, -1, 0) $ and the parametric equations of the line normal to this surface through the given point.

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