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Question

limx0((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 B 12
limx0((1cosx)+(1cosx)+(1cosx)+)1x2


Let y=((1cosx)+(1cosx)+(1cosx)+)
As x0, we can replace 1cosx with x22 as sinx can be approximated to x for small values of x
y2y=x22
2y22yx2=0
As y>0,
y=1+1+2x22
limx0((1cosx)+(1cosx)+(1cosx)+)1x2=limx01+2x212x2
Rationalizing gives
limx011+2x2+1=12
Hence, option B is the correct answer.

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