高数求极限,给个具体过程谢谢
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高数求极限,给个具体过程谢谢
原式=limx→π/2 (sinxcos3x)/(cosxsin3x),
=limx→π/2 (sinx/sin3x)*limx→π/2 (cos3x/cosx)
=limx→π/2 (sinx/sin3x)*limx→π/2 (-3sin3x/-sinx)
=limx→π/2 (sinx/sin3x)*limx→π/2 3(sin3x/sinx)
=3.
=limx→π/2 (sinx/sin3x)*limx→π/2 (cos3x/cosx)
=limx→π/2 (sinx/sin3x)*limx→π/2 (-3sin3x/-sinx)
=limx→π/2 (sinx/sin3x)*limx→π/2 3(sin3x/sinx)
=3.