Find the limit and discuss the continuity of the function. lim_{(x,y)rightarrow(3,1)}(x^2-2y)

Jaya Legge 2021-01-04 Answered
Find the limit and discuss the continuity of the function. lim(x,y)(3,1)(x22y)
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Expert Answer

irwchh
Answered 2021-01-05 Author has 102 answers
Rewiew the given function
f(x,y)=(x22y)
Objective is to find the limit when (x,y)(3,1) and discuss the continuity of the function.
To find the limit when (x,y)(3,1), solve
=lim(x,y)(3,1)(x22y)
Since the above limit is not forming any indeterminate form, so evaluate the just by substituting the value of x and y.
=(3221)
=92
=7
To check the continuity of the function
Any function f(x,y) is a continuous point (x0,y0) if lim(x,y)(x0,y0)f(x,y)=f(x0,y0)
Here
lim(x,y)(x0,y0)f(x,y)=f(x0,y0)=lim(x,y)(3,1)x22y=7 and f(x0,y0)=f(3,1)=3221=7
Since,
lim(x,y)(x0,y0)f(x,y)=f(x0,y0)=7
So, the given function is continuous at point (3,1).
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