limit -->(0,0) ((x^2)y+x^3+y^3)/(xy^2) Solution limit -->(0,0) ((x^2)y+x^3+y^3)/

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limit -->(0,0) ((x^2)y+x^3+y^3)/(xy^2) If the limit exists then it will approach the same value no matter what line you approach i along. To show that it doesn't exist you just need to find two lines where the limit approaches different values First approach the limit along the y axis ie when x=0 you get lim y^3/y^2 = lim y = 0 Next approach it along the line x=y, you get lim x^2+x^3/(x^2+x^2) = lim x^2(1+x)/(2x^2) = lim (1+x)/2 = 1/2 0 and 1/2 are different values so limit doesn't exist

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