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Differentiation question

2008 · Shift 1 · Q42

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2008 · Shift 1 · Q42

Differentiation question

2008 · Shift 1 · Q42

JEE AdvancedMathematicsDifferentiationMCQ+3 / −1

Let

f

and

g

be real valued functions defined on interval

(-1, 1)

such that

g''(x)

is continuous,

g\left( 0 \right) e 0.g'\left( 0 \right) = 0

,

g''\left( 0 \right) e 0

, and

f\left( x \right) = g\left( x \right)\sin x

STATEMENT - 1:

\mathop {\lim }\limits_{x \to 0} \,\,\left[ {g\left( x \right)\cot x - g\left( 0 \right)\csc\,x} \right] = f''\left( 0 \right)

and STATEMENT - 2:

f'\left( 0 \right) = g\left( 0 \right)

A
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
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

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