Let f and g be real valued functions defined on interval (– 1, 1) such that g ″( x ) is…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
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 : \(\lim _{x \rightarrow \infty}[g(x) \cot x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0)\)
Statement - 2 : f ′(0) = g(0).
(– 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 : \(\lim _{x \rightarrow \infty}[g(x) \cot x-g(0) \operatorname{cosec} x]=f^{\prime \prime}(0)\)
Statement - 2 : f ′(0) = g(0).
- 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.
Answer
(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
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