4. Let f(x, y) = (xy, r2 + y). Note that f(1, 2) = (2,5). (a)...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

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,

Answer 2

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