JEE Advanced 2008 Mathematics 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 : . and STATEMENT-2 : f′(0) = g(0).

(A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1Correct
(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: (A)

Solution

, so : Statement-2 is true. , so . The limit is ${g(x) x -

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-037546