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Lim((tanx-sinx)/x^3)怎么做x->0
题目详情
Lim ((tanx-sinx)/x^3)怎么做 x->0
▼优质解答
答案和解析
Lim (x-->0)((tanx-sinx)/x^3)
=lim(x-->0)(sec²x-cosx)/(3x²) (罗比达法则)
=lim(x-->0)(2secx*secxtanx+sinx)/(6x) (罗比达法则)
=lim(x-->0)(2sec³x*sinx+sinx)/(6x)
=lim(x-->0)(2sec³x+1)/6*(sinx/x)
=1/2
=lim(x-->0)(sec²x-cosx)/(3x²) (罗比达法则)
=lim(x-->0)(2secx*secxtanx+sinx)/(6x) (罗比达法则)
=lim(x-->0)(2sec³x*sinx+sinx)/(6x)
=lim(x-->0)(2sec³x+1)/6*(sinx/x)
=1/2
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