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Exercise 2 In this exercise you're going to find the linear approximation (or tangent plane, if you prefer) of the function g(x, y) = x² - y² at the point (x, y) = (1, 2). Your work should include the following steps: (a) Describe the cross sections of the surface defined by x = 1 and y = 2. (b) Find the partial derivatives of g at the appropriate point; using these values, find two vectors tangent to the surface there. (c) Give simplified parametric and cartesian equations for the tangent plane. Your writeup should include a good picture of both the surface and the tangent plane. You should put some thought into the ranges of the x- and y-values in your picture; if you're too close, you won't be able to tell the difference between the plane and the surface, but if you're too far away, the resulting picture may not be very useful. In particular, if your picture clearly shows that your plane is not tangent, or if it's impossible to tell, you will most likely lose points.

Exercise 2 In this exercise you're going to find the linear approximation (or tangent plane, if you prefer) of the function g(x, y) = x² - y² at the point (x, y) = (1, 2). Your work should include the following steps: (a) Describe the cross sections of the surface defined by x = 1 and y = 2. (b) Find the partial derivatives of g at the appropriate point; using these values, find two vectors tangent to the surface there. (c) Give simplified parametric and cartesian equations for the tangent plane. Your writeup should include a good picture of both the surface and the tangent plane. You should put some thought into the ranges of the x- and y-values in your picture; if you're too close, you won't be able to tell the difference between the plane and the surface, but if you're too far away, the resulting picture may not be very useful. In particular, if your picture clearly shows that your plane is not tangent, or if it's impossible to tell, you will most likely lose points.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Exercise 2 In this exercise you're going to find the linear approximation (or tangent plane, if you prefer) of the function g(x, y) = x² - y² at the point (x, y) = (1, 2). Your work should include the following steps: (a) Describe the cross sections of the surface defined by x = 1 and y = 2. (b) Find the partial derivatives of g at the appropriate point; using these values, find two vectors tangent to the surface there. (c) Give simplified parametric and cartesian equations for the tangent plane. Your writeup should include a good picture of both the surface and the tangent plane. You should put some thought into the ranges of the x- and y-values in your picture; if you're too close, you won't be able to tell the difference between the plane and the surface, but if you're too far away, the resulting picture may not be very useful. In particular, if your picture clearly shows that your plane is not tangent, or if it's impossible to tell, you will most likely lose points.
Transcribed Image Text:Exercise 2 In this exercise you're going to find the linear approximation (or tangent plane, if you prefer) of the function g(x, y) = x² - y² at the point (x, y) = (1, 2). Your work should include the following steps: (a) Describe the cross sections of the surface defined by x = 1 and y = 2. (b) Find the partial derivatives of g at the appropriate point; using these values, find two vectors tangent to the surface there. (c) Give simplified parametric and cartesian equations for the tangent plane. Your writeup should include a good picture of both the surface and the tangent plane. You should put some thought into the ranges of the x- and y-values in your picture; if you're too close, you won't be able to tell the difference between the plane and the surface, but if you're too far away, the resulting picture may not be very useful. In particular, if your picture clearly shows that your plane is not tangent, or if it's impossible to tell, you will most likely lose points.
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