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Question 2 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) and Statement-2 : f '(0) = g(0) Options 1. Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-1 2. Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-1 3. Statement-1 is True, Statement-2 is False 4. Statement-1 is False, Statement-2 is True

Question 2
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) and
Statement-2 : f '(0) = g(0)
Options
1. Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-1
2. Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-1
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, Statement-2 is True
 

Grade:12

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