如何求(1/(sinx)^2)-cosx^2/x^2的极限?x趋向0

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如何求(1/(sinx)^2)-cosx^2/x^2的极限?x趋向0
如何求(1/(sinx)^2)-cosx^2/x^2的极限?
x趋向0

如何求(1/(sinx)^2)-cosx^2/x^2的极限?x趋向0
原式 = lim [ x^2 - (sinx)^2(cosx)^2 ] / [ x^2 (sinx)^2 ]
= lim [ x^2 - 1/4 (sin2x)^2 ] / x^4 【sinx~x】
= lim [ x^2 - 1/8(1-cos4x) ] / x^4
= lim [ 2x - 1/2 sin4x ] / 4x^3
= lim [ 2 - 2cos4x ] / 12x^2
= lim 8sin4x / 24x
= lim 8*4x / 24x
= 4/3