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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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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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