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

Cabiolab

Cabiolab

Answered question

2021-10-13

Find the limit and discuss the continuity of the function.
lim(x,y)(1,2)x+yxy

Answer & Explanation

Cullen

Cullen

Skilled2021-10-14Added 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
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?