Differentiation

Section: Mathematics

Question : 8 of 9

Marks: +1, -0

Let f and g be real valued functions defined on interval (−1, 1) such that g″(x) is continuous, g(0) ≠ 0, g′(0) = 0, g″(0) ≠ 0, and f(x) = g(x) sin x.
STATEMENT 1:

lim

x→0

[g (x) cot x - g (0) cosec x] = f" (0)
STATEMENT 2: f ′(0) = g(0)

[JEE Adv 2008 P1]

Statement-1 is True, Statement-2 is True; Statement- 2 is a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is True; Statement- 2 is NOT a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is False.
Statement-1 is False, Statement-2 is True.

Validate

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