Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability. DEFINITIONA function f (x, y) is differentiable at a point P (xo, Yo) if, for all points (x, y) in a ô disk around P, we can writef (x, y, z) = f (xo, Yo) + fx (xo, Yo) (x – xo) + fy (Xo, Yo) (y – Yo) + E (x, y),|(4.26)where the error term E satisfiesE(x, y)= 0.lim(x.y)>(xo.Yo) /(x – x0)² + (y – yo)²

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Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 7E

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The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Show that f(x,y)=e^xyx is differentiable at point (1,0) using the definition of differentiability.

DEFINITION
A function f (x, y) is differentiable at a point P (xo, Yo) if, for all points (x, y) in a ô disk around P, we can write
f (x, y, z) = f (xo, Yo) + fx (xo, Yo) (x – xo) + fy (Xo, Yo) (y – Yo) + E (x, y),
|(4.26)
where the error term E satisfies
E(x, y)
= 0.
lim
(x.y)>(xo.Yo) /(x – x0)² + (y – yo)²

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