Answer:
Given that,
Let f(x,y)=(xy, ).
Note that f(1,20=(2,5)
(a).
Show that f has a smooth inverse in a neighborhood of the point(1,2):
and f(1,2)=(2,5)
Now,
Therefore, by the inverse function theorem, there exists a smooth inverse in a neighborhood of the point (1,2).
(b).
Find the differential matrix :
Also f(1,2)=(2,5)
We have,
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