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(a) Determine whether x-sin(y) lim (x,y) (0,0) x+y exist and evaluate it if it exist.

(a) Determine whether x-sin(y) lim (x,y) (0,0) x+y exist and evaluate it if it exist.

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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Question 1 (a) (b) Determine whether lim (x,y) (0,0) x+y exist and evaluate it if it exist. x-sin(y) Define a function f: {(x,y) = R²|mx² > (m-1)y} →→→ R by f(x, y) = e In (mx² + (1 -m)y) where m is a positive real constant. (i) (ii) Find fx and fy in terms of m. Hence, or otherwise, given that fx and fy are continuous at the point (m, m) and their values are equal there, determine the pos- sible value(s) of m.
Transcribed Image Text:Question 1 (a) (b) Determine whether lim (x,y) (0,0) x+y exist and evaluate it if it exist. x-sin(y) Define a function f: {(x,y) = R²|mx² > (m-1)y} →→→ R by f(x, y) = e In (mx² + (1 -m)y) where m is a positive real constant. (i) (ii) Find fx and fy in terms of m. Hence, or otherwise, given that fx and fy are continuous at the point (m, m) and their values are equal there, determine the pos- sible value(s) of m.
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