求x趋近于0,(tanx-sinx)/(sin^3)x的极限

问题描述:

求x趋近于0,(tanx-sinx)/(sin^3)x的极限

lim(x→0)(tanx-sinx)/(sinx)^3=lim(x→0)(1/cosx-1)/(sinx) ^2=lim(x→0)(1-cosx)/[1-(cosx)^2]cosx=lim(x→0)1/(1+cosx)cosx=1/2.