求lim(x趋于0) (tanx-sinx)/x^3

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求lim(x趋于0) (tanx-sinx)/x^3
求lim(x趋于0) (tanx-sinx)/x^3

求lim(x趋于0) (tanx-sinx)/x^3
原式为0/0型,运用洛必达法则得
lim(x趋于0) (tanx-sinx)/x^3
=lim(x趋于0) (sec^2x-cosx)/3x^2
=lim(x趋于0) (1-cos^3x)/3x^2
=lim(x趋于0) (3cos^2xsinx)/6x
=1/2