求lim(x趋于0) (tanx-sinx)⼀x^3

2024-12-22 18:09:44
推荐回答(1个)
回答1:

原式为0/0型,运用洛必达法则得
lim(x趋于0) (tanx-sinx)/x^3
=lim(x趋于0) (sec^2x-cosx)/3x^2
=lim(x趋于0) (1-cos^3x)/3x^2
=lim(x趋于0) (3cos^2xsinx)/6x
=1/2