Consider the function (a) Show that as (x, y) (0, 0) along any line y =

Question:

Consider the function f(x, y) = xy x6 + 2y

(a) Show that as (x, y) → (0, 0) along any line y = mx, the limit equals 0.

(b) Show that as (x, y) → (0, 0) along the curve y = x³, the limit does not equal 0, and hence, lim f(x, y) (x,y) (0,0) does not exist.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 16, 2024 10:00 AM

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Consider the function (a) Show that as (x, y) (0, 0) along any line y =

Question:

f(x, y) = xy + 2y x

Step by Step Answer:

a Along the line y mx the limit is If m0 this simplifies to x mx lim x0 x 2mx mx x0 x4 2m lim 0 l...View the full answer

Calculus

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