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Question

limx0((1cosx)+(1cosx)+(1cosx)+........)1x2 equals

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 C 12
Substituting gives us indeterminate form.
Differentiating the numerator,
Let, y=(1cosx+y)
y2=(1cosx+y)
2yy=sinx+y so, y=sinx2y1
Now Applying L'Hospitals Rule,
=limx0sinx(2y1)2x
Substituting gives us indeterminate form, so applying L'Hospitals Rule,
=limx0cosx(4xy+4y2)
=12(y=1 when x=0)
Hence, option 'B' is correct.

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