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dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that it agrees with the result obtained by substitution for x and y before differentiating.

dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that it agrees with the result obtained by substitution for x and y before differentiating.

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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If z = e2x+ 3yand x = In t, y = t², calculate dz from the total dt derivative formula and show that it agrees with the result obtained by substitution for x and y before differentiating.
Transcribed Image Text:If z = e2x+ 3yand x = In t, y = t², calculate dz from the total dt derivative formula and show that it agrees with the result obtained by substitution for x and y before differentiating.
Use completing square method to identify the type of equation and coordinates in the equation x² + yv² + z² – 4x + 2y = 0. a. (a,b,c) = (2,-1, 3) is the centre of the sphere b. (a,b,c) = (2,-1, 0) is the centre of the sphere c. (a,b,c) = (3,-1, 0) is the centre of the sphere d. (a,b,c) = (2,1, 1) is the centre of the sphere e. (a,b,c) = (2,0, 3) is the centre of the sphere
Transcribed Image Text:Use completing square method to identify the type of equation and coordinates in the equation x² + yv² + z² – 4x + 2y = 0. a. (a,b,c) = (2,-1, 3) is the centre of the sphere b. (a,b,c) = (2,-1, 0) is the centre of the sphere c. (a,b,c) = (3,-1, 0) is the centre of the sphere d. (a,b,c) = (2,1, 1) is the centre of the sphere e. (a,b,c) = (2,0, 3) is the centre of the sphere
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