Saturday, 14 May 2016

calculus - Evaluating limxto0fracsin(4x)sin(3x) without L'Hospital




I need to evaluate
limx0sin(4x)sin(3x)


I solved this using L'Hospital's Theorem and I got 4/3
However, is there a way to do this without applying this theoerm?


Answer



As limx0sin(x)x=1


limx0sin(4x)sin(3x)
can be written as
43limx0sin(4x)4x3xsin(3x)

=43



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