Question

求极限：lim 2(x+1)arctan(1/x) (x趋于0 )

Answer 1

用极限的运算法则就行.

lim(x→0)2(x+1)=2

lim(x→0)arctan(1/x) =π/2

所以lim(x→0)2(x+1)arctan(1/x)=[lim(x→0)2(x+1)][lim(x→0)arctan(1/x)]=2×π/2=π

注：y=arctanx是一个增函数,x∈(-∞,+∞),y∈(-π/2,π/2)