The limit of [(1 / X of 2 + e) / (2 / X of 1 + e) + |x | / x] when x tends to zero

The limit of [(1 / X of 2 + e) / (2 / X of 1 + e) + |x | / x] when x tends to zero

(x->0)lim[2+e^(1/x)]/[(1+e^(2/x)] + |x|/x
=(T - > ∞) LIM (2 + e ^ t) / (1 + e ^ 2t) + T / | t | transformation variable t = 1 / X
=(t->∞)lim(2/e^t+1)/(1/e^t+e^t) + t/|t|
=(t->∞)lim 1/e^t + t/|t|
=(t->∞)lim t/|t|
T - > + ∞, the original formula is 1
T - > - ∞, primitive = - 1
So there is no limit in the original formula