By considering different path of approach, show that the function f(x,y)=(x^2+y)/y has no limis (x,y) ->(0,0)

slaggingV 2021-01-02 Answered
By considering different path of approach, show that the function f(x,y)=x2+yy has no limis (x,y)(0,0)
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un4t5o4v
Answered 2021-01-03 Author has 105 answers
It is known that when finding the limits of the multivariable function we have to find the limits using different paths .
Take the path along the x-axis ,then (x,y)(x,0)
lim(x,y)(x,0)f(x)lim((x,y)(x,0))x2+yy=0
Take the path along the y-axis ,then
lim(x,y)(x,0)f(x)lim((x,y)(x,0))x2+yy=1
Using the different paths , the values of the limits is different , then the limit does not exist.
Thus, the given function f(x,y)=x2+yy has no limits
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