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.
Comments
Leave a comment