Answer to Question #249068 in Calculus for Nikki

Question #249068
What is limit of (x,y) tends to (0,0) 1/sinxy?
1
Expert's answer
2021-10-12T09:39:53-0400

Along "x=y"


"\\lim\\limits_{(x, y)\\to(0,0)}(\\dfrac{1}{\\sin(xy)})=\\lim\\limits_{(x, y)\\to(0,0)}(\\dfrac{1}{\\sin(x^2)})=\\infin"

Along "x=-y"


"\\lim\\limits_{(x, y)\\to(0,0)}(\\dfrac{1}{\\sin(xy)})=\\lim\\limits_{(x, y)\\to(0,0)}(\\dfrac{1}{\\sin(-x^2)})=-\\infin"

Therefore "\\lim\\limits_{(x, y)\\to(0,0)}(\\dfrac{1}{\\sin(xy)})" does not exist.


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