let f(x,y)=y/(x^2-y) for (x,y)=(0,0) .It is possible to define f(0,0) in a way t

ID: 3215192 • Letter: L

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let f(x,y)=y/(x^2-y) for (x,y)=(0,0) .It is possible to define f(0,0) in a way that makes f continuous at the origin ? Explain your answer.

Explanation / Answer

for f(x,y) to be continous lim x,y--->0 f(x,y) from left side shd be equal to f(x,y) from right side shd be equal to f(x,y) clearly f(x,y) from left = f(x,y) from right now to define f(0,0)we just need the limit as (x,y) ---> 0 ,0 so lim (x,y)--->0,0 = the equation is of the form 0/0 use l-hospitals rule u get f(x,y) = 1/2x-1 as x---> 0 this will be 1/-1 = -1 so lim x,y ----> 0,0 f(x,y) = -1 so define f(0,0)as -1 for this function to be continous

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let f(x,y)=y/(x^2-y) for (x,y)=(0,0) .It is possible to define f(0,0) in a way t

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