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lim(tanx)^cosxx趋于派/2
题目详情
lim(tanx)^cosx x趋于派/2
▼优质解答
答案和解析
lim(x→π/2) (tanx)^cosx
=lim(x→π/2) e^[ln(tanx)^cosx]
=lim(x→π/2) e^[ln(tanx)*cosx]
=lim(x→π/2) e^[ln(tanx)/secx]
=lim(x→π/2) e^[sec^2x/(tanx*secx*tanx)]
=lim(x→π/2) e^[1/(tanx*cosx*tanx)]
=lim(x→π/2) e^[1/(sinx*tanx)]
=1
=lim(x→π/2) e^[ln(tanx)^cosx]
=lim(x→π/2) e^[ln(tanx)*cosx]
=lim(x→π/2) e^[ln(tanx)/secx]
=lim(x→π/2) e^[sec^2x/(tanx*secx*tanx)]
=lim(x→π/2) e^[1/(tanx*cosx*tanx)]
=lim(x→π/2) e^[1/(sinx*tanx)]
=1
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