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y-1 = x²y-xy-x²+x f(x,y) (i) f is continuous at every point of its domain (ii) the domain of f is the entire plane expect the origin. (iii) The limit of f approaches ∞ as (x,y) -> (1,1) (iv) the domain of f is the set of points in the plane whose x and y coordinates are different from 1 and x coordinates are

y-1 = x²y-xy-x²+x f(x,y) (i) f is continuous at every point of its domain (ii) the domain of f is the entire plane expect the origin. (iii) The limit of f approaches ∞ as (x,y) -> (1,1) (iv) the domain of f is the set of points in the plane whose x and y coordinates are different from 1 and x coordinates are

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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f(x, y) = x²y_xy_x²+x y-1 (i) f is continuous at every point of its domain (ii) the domain of f is the entire plane expect the origin. (iii) The limit of f approaches ∞ as (x,y) -> (1,1) (iv) the domain of f is the set of points in the plane whose x and y coordinates are different from 1 and x coordinates are nonzero. (v) lim(x,y)->(-1,1) f (x,y) exists but f is not continuous at (-1,1)
Transcribed Image Text:f(x, y) = x²y_xy_x²+x y-1 (i) f is continuous at every point of its domain (ii) the domain of f is the entire plane expect the origin. (iii) The limit of f approaches ∞ as (x,y) -> (1,1) (iv) the domain of f is the set of points in the plane whose x and y coordinates are different from 1 and x coordinates are nonzero. (v) lim(x,y)->(-1,1) f (x,y) exists but f is not continuous at (-1,1)
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