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Let f :[1,oo] to[2,oo]differentiable function such that f (1) = 2 .If [1,oo] to[2,oo] |
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Answer» `rArr6(x)*1-0=3f(x)+3xf'(x)-3x^(2)` `RARR 3xf' (x) -3 f(x) = 3x^(2) rArr f' (x) -(1)/(x)f(x)=x` `rArr (xf'(x)-f'(x))/(x^(2))=1rArr (d)/(dx){(x)/(x)}=1` On INTEGRATING both sides , we get `rArr (f(x))/(x')=x+c`"" [`:' f(1)=(1)/(3)]` `(1)/(3)=1+crArrc=(2)/(3)ANDF(x)=x^(2)-(2)/(3)x` `:. f(2)=4-(4)/(3)=(8)/(3)` NOTEHere , f (1) = 2 , does not satisfy given function. `:. f(1) = (1)/(3)` For that f (x)`=x^(2)-(2)/(3)x andf(2)=4-(4)/(3)=(8)/(3)` |
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