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Sarita Math

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Sep 20, 2012, 9:14:01 AM9/20/12
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AMAN GUPTA

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Sep 21, 2012, 10:48:48 AM9/21/12
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8. Check the existence of implicit functions at the given point:
a). f(x; y) = y2 􀀀 x2y 􀀀 2x5 at (0, 0).
b). f(x; y) = y2 + 2x2y + x5 at (1,-1).
c). f(x; y) = 2xy 􀀀 log(xy) 􀀀 2 at (1,1).  how to these type of  question


On Thu, Sep 20, 2012 at 6:44 PM, Sarita Math <sarita...@gmail.com> wrote:
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Sarita Math

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Sep 21, 2012, 12:15:05 PM9/21/12
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Apply "Implicit function theorem for two variables" which states that






Solved problem:

c) .

Ans. Here 
Hence f(x,y) =0 gives y as a function of x in neighbourhood of the point (1,1).
 
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