Let $f$ and $g$ be real valued functions defined on interval $(-1,1)$ such that $g^{\prime \prime}(x)$ is continuous, $g(0) \neq 0, g^{\prime}(0)=0, g^{\prime \prime}(0) \neq$ 0 , and $f(x)=g(x) \sin x$.
$STATEMENT$ $-1: \lim _{x \rightarrow 0}[g(x) \cot x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0)$.and
$STATEMENT$ $-2: f^{\prime}(0)=g(0)$.
Let $f$ and $g$ be real valued functions defined on interval $(-1,1)$ such that $g^{\prime \prime}(x)$ is continuous, $g(0) \neq 0, g^{\prime}(0)=0, g^{\prime \prime}(0) \neq$ 0 , and $f(x)=g(x) \sin x$.
$STATEMENT$ $-1: \lim _{x \rightarrow 0}[g(x) \cot x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0)$.and
$STATEMENT$ $-2: f^{\prime}(0)=g(0)$.
- [IIT 2008]
- A
Statement-$1$ is True, Statement -$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$
- B
Statement -$1$ is True, Statement - $2$ is True; Statement-$2$ is $NOT$ a correct explanation for Statement-$1$
- C
Statement -$1$ is True, Statement -$2$ is False
- D
Statement -$1$ is False, Statement -$2$ is True
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