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1.9. The function (, , ) = 3 + + + 2 is infinitely differentiable.If we prove that the partial derivative with respect to is always nonzero,the corresponding theorem will guarantee us a unique continuous solution for of (, , ) = 0.It is simple to prove:= 2 2 + + + > 0.11. = [0, 1] [0, 1] 2 , (, ) = (5 ( 2 + 2 ),15).To prove it is a contraction from to we need to prove that if (, ) then (, ) .11It is true: denote (, ) = 5 ( 2 + 2 ) (the x-component), (, ) = 5 (the y-component).2155Then 0 (, ) , 0 (, ) and thus (, ) .And we need to ...


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