求极限x趋向于0 (1-cos2x)/xsinx

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求极限x趋向于0(1-cos2x)/xsinx求极限x趋向于0(1-cos2x)/xsinx求极限x趋向于0(1-cos2x)/xsinxlim(x→0)(1-cos2x)/xsinx=lim(x→0

求极限x趋向于0 (1-cos2x)/xsinx
求极限x趋向于0 (1-cos2x)/xsinx

求极限x趋向于0 (1-cos2x)/xsinx
lim(x→0)(1-cos2x)/xsinx
=lim(x→0) (x^2/2)/x^2
=1/2

=lim{1-[1-2(sinx)^2]}/xsinx
=lim2sinx/x
=2

用等价无穷小做:当x→0时 1-cos(2x)~(1/2)x²
sin(x)~x
所以 lim(x→0)(1-cos2x)/xsinx
=lim(x→0) (x^2/2)/x^2
=1/2