Find the limit and discuss the continuity of the function. \lim_{(x,y)\to

Cabiolab 2021-10-13 Answered
Find the limit and discuss the continuity of the function.
lim(x,y)(1,2)x+yxy
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Expert Answer

Cullen
Answered 2021-10-14 Author has 89 answers
Consider the given limit lim(x,y)(1,2)x+yxy
Now find the limit
lim(x,y)(1,2)x+yxy=1+212
=13
=13
So limit is lim(x,y)(1,2)x+yxy=13
Condition for continuity lim(x,y)(a,b)f(x,y)=f(a,b)
Find the value of the function at the given limit point
f(x,y)=x+yxy
f(1,2)=1+212
=13
=13
So, lim(x,y)(1,2)x+yxy=f(1,2)=13
Hence function is continuous at the given limit point
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