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1. The equation r²y³ +2ln(yz) + ye" - 1 determines a surface. Note that you cannot easily write z as a function of a and y. (a) Use implicit differentiation to find at the point (0,1,2). (b) Use implicit differentiation to find at the point (0,1,2).

1. The equation r²y³ +2ln(yz) + ye" - 1 determines a surface. Note that you cannot easily write z as a function of a and y. (a) Use implicit differentiation to find at the point (0,1,2). (b) Use implicit differentiation to find at the point (0,1,2).

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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1. The equation r²y³ +2ln(yz) + ye™² - 1 determines a surface. Note that you cannot easily write z as a function of a and y. (a) Use implicit differentiation to find at the point (0,1,2). (b) Use implicit differentiation to find at the point (0,1,2). 2. A right triangle has sides of length a abd b and a hypotenuse of length c. Suppose the triangle initially has a 5 and 6-12 but then the smaller side length increases to 5.1 while the longer side decreases to 11.8. By how much does the hypotenuse's length change? 3. Find equation of the tangent plane to f(x,y) - e²+² at the point (1,1) and use it to approximate the value of ee¹² +2²
Transcribed Image Text:1. The equation r²y³ +2ln(yz) + ye™² - 1 determines a surface. Note that you cannot easily write z as a function of a and y. (a) Use implicit differentiation to find at the point (0,1,2). (b) Use implicit differentiation to find at the point (0,1,2). 2. A right triangle has sides of length a abd b and a hypotenuse of length c. Suppose the triangle initially has a 5 and 6-12 but then the smaller side length increases to 5.1 while the longer side decreases to 11.8. By how much does the hypotenuse's length change? 3. Find equation of the tangent plane to f(x,y) - e²+² at the point (1,1) and use it to approximate the value of ee¹² +2²
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