Question

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 : $\underset{x \rightarrow 0}{lim}$[g(x) cot x – g(0) cosec x] = f"(0) and
STATEMENT - 2 : f '(0) = g(0)
(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

Answer 1

Answer:dfividfuvnidfuvfiuvfiuvdfivudfviudfviufnviuvnidfuvndfiuvnfivundfivudfnvidufnvifduvndivunfivunStep-by-step explanation: