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Differential Calculus

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30 Jul 2007 18:22:28 IST

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plz solve this

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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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Titun

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Joined: 23 Dec 2006

Posts: 374

30 Jul 2007 19:00:52 IST

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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!

sudip banerjee

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Joined: 10 Jun 2007

Posts: 9

2 Aug 2007 09:56:25 IST

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thanx very much titun. ur soln was wonderful

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