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Let f and g be real valued functions def...

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)sinx` . Statement-1 : `("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0)` and Statement-2 : `f'(0)=g(0)`

A

Statement-1 is True, Statement -2 is True, Statement -2 is True and Statement -2 is a correct explanation for statement -1.

B

Statement -1 is True, Statement -2 is True and Statement -2 is Not is a correct explanation for Statement -1.

C

Statement -1 is True, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

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The correct Answer is:
B
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