x趋于0的时候,arctan(1/x) 的极限是π/2(x趋于0+)或者-π/2(x趋于0-)由lim(x→0-)xarctan(1/x)=lim(x→0-)x × lim(x→0-)arctan(1/x)=0 × (-π/2)=0由lim(x→0+)xarctan(1/x)=lim(x→0+)x × lim(x→0+)arctan(1/x)=0 × (π/2)=0故:lim(x→0)xarctan(1/x)=0所以为可去间断点