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Question

Evaluate the limit:

limx0sin(3+x)sin(3x)x

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Solution

We have

limx0sin(3+x)sin(3x)x

It becomes 0/0 form.

[sinAsinB=2cosA+B2sinAB2]

=limx02cos(3+x+3x2)sin(3+x3+x2)x

=limx02cos3 sinxx

=2cos3limx0sinxx [limx0sinxx=1]

=2cos3×1

=2cos3

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