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![[Post New]](/templates/default/images/icon_minipost_new.gif) 30 Jul 2007 18:22:28 IST
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given f'(x)=g(x) and g'(x)= -f(x). and f(2)=4=f'(2). find the value of f^2(16)+ g^2(16)=........... ans: 32. plz give complete soln.
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f ' (x) = g (x)
g ' (x) = - f (x)
Consider a function
h (x) = [ f (x) ] 2 + [ g (x) ] 2
Therefore, h ' (x) = 2 f (x) . f ' (x) + 2 g(x). g ' (x) = 2 f (x). g(x) - 2 g(x). f (x) = 0
Hence, h (x) is a constant function and so the value of h (2) will be the same as the value of h (16)
h (2) = [ f (2) ] 2 + [ g (2) ] 2 = [ f (2) ]2 + [ - f (2) ] 2 = 42 + 42 = 32
h (2) = h (16) = 32
So, h (16) = [ f (16) ] 2 + [ g (16) ] 2 = 32
Cheers!
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You never know what is enough till you know what is more than enough.
Titun |
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2 Aug 2007 09:56:25 IST
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thanx very much titun. ur soln was wonderful
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