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Question

Ltx0f(1cos3xx2) where f(x) is a continuous function satisfying the condition f(92)=29 is equal to:

A
0
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B
9/2
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C
2/9
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D
4
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Solution

The correct option is D 2/9

cosx=1x22!+x44!cos(3x)=1(3x)22!+(3x)44!=limx0f⎢ ⎢ ⎢ ⎢1(19x22!+34x44!....)x2⎥ ⎥ ⎥ ⎥=limx0f⎢ ⎢ ⎢ ⎢9x22!+34x44!....x2⎥ ⎥ ⎥ ⎥=limx0f[92!+34x44!+36x46!...]=f[92!0+0...]=f[9x22!]=f[9x22!]=29


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