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Question

limx⎜ ⎜ ⎜ ⎜(1cosx)+(1cosx)+(1cosx)+...)1x2⎟ ⎟ ⎟ ⎟ equals to

A
0
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B
12
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C
1
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D
2
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Solution

The correct option is D 12
Let (1cosx)+(1cosx)+(1cosx)+...)=y

y=(1cosx)+y

y2y+(cosx1)=0

y=1+54cosx2

Now required limit is limx0 1+54cosx12x2 =12

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