Let f : R → R be a differentiable function satisfying f ' 3 + f ' 2 = 0 . Then l i m x → 0 1 + f 3 + x - f 3 1 + f 2 - x - f 2 1 x is equal to

Question

Let f : R → R be a differentiable function satisfying f ' 3 + f ' 2 = 0 . Then l i m x → 0 1 + f 3 + x - f 3 1 + f 2 - x - f 2 1 x is equal to, 1, e, e 2, e - 1

MARKS App · Accepted Answer

This limit is 1 ∞ form ∴ l i m x → 0 1 + f 3 + x - f 3 1 + f 2 - x - f 2 1 x = e l i m x → 0 1 x 1 + f 3 + x - f 3 1 + f 2 - x - f 2 - 1 = e l i m x → 0 1 x f 3 + x - f 3 - f 2 - x + f 2 1 + f 2 - x - f 2 0 0 f o r m = e l i m x → 0 f ' 3 + x + f ' 2 - x x - f ' 2 - x + 1 + f 2 - x - f 2 = e 0 = 1 .

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