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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

(a) Write an expression as a limit for the directional derivative of f at (x0, y0) in the direction of a unit vector u = ⟨a, b⟩. How do you interpret it as a rate? How do you interpret it geometrically?

(b) If f is differentiable, write an expression for Duf(x0, y0) terms of fx and fy.

(a)

To determine

To write: The expression as a limit for the directional derivative of f at (x0,y0) in the direction of a unit vector u=a,b . Interpret its rate of change. Also interpret it geometrically.

Explanation

The directional derivative Duf(x0,y0) of f(x,y) at (x0,y0) in the direction of a unit vector u=a,b is Duf(x0,y0)=limh0f(x0+ha,y0+hb)f(x0,y0)h

(b)

To determine

To write: The expression for the directional derivative Duf(x0,y0) in terms of fxandfy .

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Chapter 14 Solutions

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