lim(x趋近于0)(（1/sin^2 x）-(cos^2 x)/x^2)=
第1个回答 2020-05-16
lim(x→0)(（1/sin^2 x）-(cos^2 x)/x^2)
=lim(x→0) ((x^2-sin^2xcos^2x)/x^2*sin^2x)
=lim(x→0)((x^2-1/4sin^2(2x))/x^4) sinx与x等价无穷小量,再用
罗必塔 =lim(x→0)(2x-1/2sin4x)/4x^3
=lim(x→0)(2-2cos4x)/12x^2
=lim(x→0)(8sin4x/24x)
=lim(x→0)(32cos4x/24)
=32/24=4/3
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