Question

高数 求极限？

limit(xarccotx) as x->0

Answer 1

x趋于零时，arccotx趋于无穷，
极限为零乘以无穷的形式，可以运用洛必达法则如下望采纳
|imarccotx/(1/x)
=limx^2/(1+x^2)
=0

Answer 2

lim(x->0) x.arccotx
=lim(x->0) arccotx /(1/x) (∞/∞ 分子分母分别求导)
=lim(x->0) [-1/(1+x^2)] /(-1/x^2)
=lim(x->0) x^2/(1+x^2)
=0