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Let f and g be real valued functions def...

Let f and g be real valued functions defined on interval `(-1, 1)` such that g'' (x) is continuous, ` g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x`.
Statement I `underset( x to 0) lim [g(x) cos x - g(0)] [cosec x] = f''(0)`. and
Statement II f'(0) = g(0).

A

Statement (1) is true and statement (2) is true and statement (2) is correct explanation for statement (1)

B

Statement (1) is true and statement (2) is true and statement (2) is NOT a correct explanation for Statement (1)

C

Statement (1) is true but (2) is false

D

Statement (1) is false but (2) is true

Text Solution

Verified by Experts

The correct Answer is:
B
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