lim(x→1-）e^1/(x-1)+3=3
lim(x→1+）e^1/(x-1)+3=∞
lim(x→1）3+(x-1)sin1/(x-1)
sin1/(x-1)是有界函数,而x-1→0
所以
lim(x→1）3+(x-1)sin1/(x-1)＝3