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).

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

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

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

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

Verified by Experts

The correct Answer is:

CONTINUITY
MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR JEE MAIN|4 Videos
COMPLEX NUMBER
MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos
DEFINITE INTEGRATION
MOTION|Exercise EXERCISE -4 LEVEL-II|33 Videos

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 lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

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

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

Statement I is true, Statement II is false

Statement I is false, Statement II is true

Both statement I and Statement II are correct and Statement II is the correct explanation of Statement I

Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I

Statement I is correct but Statement II is incorrect

Statement II is correct but Statement I is incorrect.

`-x`

None of these