a) Find the equation of the tangent plane to z = f (x, y) = 3x² + 2y² +5 at the point (1,1,10). b) Use the linear approximation of z = f(x, y) at (1,1,10) to approximate the value of f(0.05, 1.05). Round to 3 decimal places. c) What is the angle between the tangent planes to z = f(x, y) = 3x² + 2y² +5 at (0,0,5) and (1,1,10)? Round to the nearest 10th of a degree.

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...
Question
a) Find the equation of the tangent plane to z = f (x, y) =
3x² + 2y² +5 at the point (1,1,10).
b)
Use the linear approximation of z = f(x, y) at (1,1,10) to
approximate the value of f(0.05, 1.05). Round to 3 decimal
places.
c)
What is the angle between the tangent planes to
z = f(x, y) = 3x² + 2y² +5 at (0,0,5) and (1,1,10)? Round
to the nearest 10th of a degree.
Transcribed Image Text:a) Find the equation of the tangent plane to z = f (x, y) = 3x² + 2y² +5 at the point (1,1,10). b) Use the linear approximation of z = f(x, y) at (1,1,10) to approximate the value of f(0.05, 1.05). Round to 3 decimal places. c) What is the angle between the tangent planes to z = f(x, y) = 3x² + 2y² +5 at (0,0,5) and (1,1,10)? Round to the nearest 10th of a degree.
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