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【高数问题求解‼lim(tanx-sinx)/(sinx)^3.x趋向0】
高数问题求解‼lim(tanx-sinx)/(sinx)^3.x趋向0
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2020-01-23 17:30
【高数问题求解‼lim(tanx-sinx)/(sinx)^3.x趋向0】
高数问题求解‼lim(tanx-sinx)/(sinx)^3.x趋向0
lim(x→0)(tanx-sinx)/(sinx)^3
=lim(x→0)(tanx-sinx)/x^3,分母等价无穷小
=lim(x→0)sinx(1/cosx-1)/x^3
=lim(x→0)(sinx)/x*(1-cosx)/(x^2*cosx)
=lim(x→0)2[sin(x/2)]^2/x^2
=lim(x→0)[sin(x/2)]^2/(x/2)^2*1/2
=1/2