Find the limit (if it exists) and discuss the continuity of the function. \lim_{(x, y)→(0, 0)} \frac{y+xe^{-y²}}{1+x²}

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-05-16

Find the limit (if it exists) and discuss the continuity of the function. lim(x,y)(0,0)y+xey²1+x²

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-05-17Added 105 answers

The continuity and limit of the two variable function
lim(x,y)(0,0)y+xey²1+x²
According to the continuity equation of two variable have to follow
lim(x,y)(x0,y0)f(x,y)=f(x0,y0) Here we have to check whether it is follow or not
lim(x,y)(0,0)y+xey²1+x²=0andf(0,0)=0
Thus the given function is continuous in the open region R which means there is no point of discontinuous and limit of function
lim(x,y)(0,0)y+xey²1+x²=0
exist that is 0

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