lim x趋于0[(tanx-sinx)/sinx^3]的极限
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lim x趋于0[(tanx-sinx)/sinx^3]的极限
=lim(1/cosx-1)/(sinx)^2
=lim(1-cosx)/(sinx)^2cosx
=lim2(sin(x/2))^2/(sinx)^2
=(1/2)lim[(sin(x/2))^2/(x/2)^2][x^2/(sinx)^2]
=1/2
lim(x→0)[(tanx-sinx)/(sinx)^3]
=lim(x→0)[(sinx/cosx-sinx)/(sinx)^3]
=lim(x→0)[(1/cosx-1)/(sinx)^2]
=lim(x→0){(1-cosx)/[cosx(sinx)^2]}
=lim(x→0)(1/cosx)(1-cosx)/[1-(cosx)^2]
=lim(x→...
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lim(x→0)[(tanx-sinx)/(sinx)^3]
=lim(x→0)[(sinx/cosx-sinx)/(sinx)^3]
=lim(x→0)[(1/cosx-1)/(sinx)^2]
=lim(x→0){(1-cosx)/[cosx(sinx)^2]}
=lim(x→0)(1/cosx)(1-cosx)/[1-(cosx)^2]
=lim(x→0)(1/cosx)(1-cosx)/[(1+cosx)(1-cosx)]
=lim(x→0)(1/cosx)[1/(1+cosx)]
=1×[1/(1+1)]
=1/2。
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=lim(1/cosx-1)/(sinx)^2
=lim(1-cosx)/(sinx)^2cosx
=lim2(sin(x/2))^2/(sinx)^2
=(1/2)lim[(sin(x/2))^2/(x/2)^2][x^2/(sinx)^2]
=1/2
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