极限导数-这四个极限具体怎么求出来的？

Question

rt，求学霸解答下，感谢

Answer 1

eˣ/(eˣ-1)=(eˣ-1+1)/(eˣ-1)=1+1/(eˣ-1)

x→0-,(eˣ-1)→0- 1/(eˣ-1)→-∞
x→0+,(eˣ-1)→0+ 1/(eˣ-1)→+∞
x→+∞ (eˣ-1)→+∞ 1/(eˣ-1)→0
x→-∞ (eˣ-1)→-1 1/(eˣ-1)→-1