2.5计算极限lim(x→0) (1-cos2x)/xsinx
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2.5计算极限lim(x→0)(1-cos2x)/xsinx2.5计算极限lim(x→0)(1-cos2x)/xsinx2.5计算极限lim(x→0)(1-cos2x)/xsinxcos2x=1-2s
2.5计算极限lim(x→0) (1-cos2x)/xsinx
2.5计算极限lim(x→0) (1-cos2x)/xsinx
2.5计算极限lim(x→0) (1-cos2x)/xsinx
cos2x=1-2sin²x
(1-cos2x)/xsinx=[1-((1-2sin²x)]/xsinx
=2sin²x/xsinx
=2sinx/x
lim(x→0) (1-cos2x)/xsinx=lim(x→0) 2sinx/x=2
先利用 x等价于sinx有
原式 = lim (1-cos2x)/x²
=lim 2sin2x / 2x (洛毕塔法则)
=lim 2x/x
=2
lim(x→0) (1-cos2x)/xsinx
=lim(x→0) [2(sinx)^2]/xsinx
=lim(x→0) 2sinx/x
=2
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