How to prove that the limit of x [1 / x] is 1 when limx tends to 0

How to prove that the limit of x [1 / x] is 1 when limx tends to 0


Let [1 / x] = n, then n=



Why is the left limit of e ^ (1 / x) 0 when limx tends to 0


x-->0- 1/x-->-∞
e^(1/x)-->e^(-∞)-->0



Find the limit of limx tending to 0 (1-x) ^ (2 / x)


limx→0(1-x)^2/x
=limx→0(1+(-x))^(-1/x)*(-2)
=[limx→0(1+(-x))^(-1/x)*]^(-2)
=e^(-2)