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Question

limx0(10sin9x9sin10x)(8sin7x7sin8x)(6sin5x5sin6x)(4sin3x3sin4x)(sinxsin2x) is equal to

A
63256
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B
16
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C
65
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D
12
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E
25663
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Solution

The correct option is E 65
limx0(109sin9xsin10x)(87sin7xsin8x)(65sin5xsin6x)(43sin3xsin4x)(sinxsin2x)
=limx0⎜ ⎜ ⎜sin9x9x1sin10x10x⎟ ⎟ ⎟⎜ ⎜ ⎜sin7x7x1sin8x8x⎟ ⎟ ⎟⎜ ⎜ ⎜sin5x5x1sin6x6x⎟ ⎟ ⎟⎜ ⎜ ⎜sin3x3x1sin4x4x⎟ ⎟ ⎟⎜ ⎜ ⎜sinxx1sin2x2x12⎟ ⎟ ⎟
=12 [limf(x)0sinf(x)f(x)=1]

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