Question

求xsinx/1-cos3x x趋向于0的极限

Answer 1

x→0

lim (xsinx)/(1-cos3x)

此极限为0/0型,根据L'Hospital法则

=lim (xsinx)'/(1-cos3x)'

=lim (sinx+xcosx) / (3sin3x)

此极限为0/0型,根据L'Hospital法则

=lim (sinx+xcosx)' / (3sin3x)'

=lim (cosx+cosx-xsinx) / (9cos3x)

=lim (2cosx-xsinx)/(9cos3x)

=(2-0)/(9*1)

=2/9

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