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lim(1/sin^2x-cos^2x/x^2),其中x→0
题目详情
lim(1/sin^2 x - cos^2 x/x^2),其中x→0
▼优质解答
答案和解析
原式=lim(x→0)[(x^2-(sinxcosx)^2)/(x^2sin^2x)
=lim(x→0)[(x^2-1/4(sin2x)^2)/(x^4)
=lim(x→0)[2x-sin2xcos2x]/4x^3
=lim(x→0)[2-2cos4x]/12x^2
=lim(x→0)[8sin4x]/24x
=lim(x→0)[32cox4x]/24
=32/24=4/3
=lim(x→0)[(x^2-1/4(sin2x)^2)/(x^4)
=lim(x→0)[2x-sin2xcos2x]/4x^3
=lim(x→0)[2-2cos4x]/12x^2
=lim(x→0)[8sin4x]/24x
=lim(x→0)[32cox4x]/24
=32/24=4/3
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