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Question

limx0sin(6x2)lncos(2x2x) is equal to

A
12
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B
12
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C
6
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D
6
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Solution

The correct option is B 12

We have,

limx0(sin(6x2)ln(cos(2x2x)))

This is the 00 form.

So, apply L-Hospital rule

limx0⎜ ⎜ ⎜ ⎜cos(6x2)×(12x)1cos(2x2x)×(sin(2x2x))×(4x1)⎟ ⎟ ⎟ ⎟

limx0(12xcos(6x2)tan(2x2x)×(4x1))

This is the 00 form.

So, apply L-Hospital rule

limx0(12xcos(6x2)(4x1)tan(2x2x))

limx0(12cos(6x2)+12x(sin(6x2))×12x(4x1)sec2(2x2x)×(4x1)tan(2x2x)(40))

limx0(12cos(6x2)144x2sin(6x2)(4x1)2sec2(2x2x)4tan(2x2x))

=12cos00(01)2sec204tan0

=1210

=12

Hence, this is the answer.


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