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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(x) sin x`.
Statement I `lim_(xto0) [g(x) cos x - g(0) "cosec x"] = f''(0)`. and
Statement II f'(0) = g(0).
For the following questions, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows.

A

Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I

B

Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I

C

Statement I is true, Statement II is false

D

Statement I is false, Statement II is true

Text Solution

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The correct Answer is:
B
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