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|im(x一兀/2)tanxx→兀/2求极限
题目详情
|im(x一兀/2)tanx x→兀/2 求极限
▼优质解答
答案和解析
记t=x-π/2
则原式=lim(t->0) t*tan (t+π/2)
=lim(t->0)-t* cott
=lim(t->0)-tcost/sint
=lim(t->0) -t/sint
=-1
则原式=lim(t->0) t*tan (t+π/2)
=lim(t->0)-t* cott
=lim(t->0)-tcost/sint
=lim(t->0) -t/sint
=-1
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