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Let `f : R to R ` be a differentiable function satisfying `f'(3) + f'(2) = 0 `, Then `underset(x to 0) lim ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) ` is equal to

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`lim _ (xto 0)((l + f (3 + x) - f (3))/( 1 + f (2 - x ) - f (2))) ^ ((1)/(x)) rArr = e ^(lim_ ( x to 0) ((1 + f ( 3 + x ) - f (3 ) )/( 1 + f (2 - x ) - f (2))- 1 ) (1 )/(x) `
`= e^(f' (3) + f' (2)) = e ^0 = 1 `
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