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z+y <=0. (a) Using - definition, show that lim (a)+(0,0) 2²+ y² +1 [2²sin +3² sin, (2, 3) (0,0) (b) Show that the function f(x, y) defined by f(x, y) = 0, (z,y) = (0,0) differentiable at (0,0).

z+y <=0. (a) Using - definition, show that lim (a)+(0,0) 2²+ y² +1 [2²sin +3² sin, (2, 3) (0,0) (b) Show that the function f(x, y) defined by f(x, y) = 0, (z,y) = (0,0) differentiable at (0,0).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. (a) Using - definition, show that x+y lim (z.y)-(0,0) x² + y² +1 <= 0. [2²sin+y²sin, (2.9) # (0,0) (b) Show that the function f(x, y) defined by f(x, y) = (x, y) = (0,0) differentiable at (0,0). əz 2. (a) If ==y+(u), then fut (by Usefreiors them to find a livent approximatisa of fo Estimat ay at the origi The apprimati - and- Here (u) is a differentiable function.
Transcribed Image Text:1. (a) Using - definition, show that x+y lim (z.y)-(0,0) x² + y² +1 <= 0. [2²sin+y²sin, (2.9) # (0,0) (b) Show that the function f(x, y) defined by f(x, y) = (x, y) = (0,0) differentiable at (0,0). əz 2. (a) If ==y+(u), then fut (by Usefreiors them to find a livent approximatisa of fo Estimat ay at the origi The apprimati - and- Here (u) is a differentiable function.
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