Limits at infinity with e

Question

lim--> -infty (4+6e^2t)/(5-9e^3t)

 

I really dont understand it

Answer 1

Limit as t → -∞ of (4 + 6e^2t) / (5 - 9e^3t) = ?

 

Note that as  t → -∞, e^2t → 0 and e^3t → 0

 

Then

 

limit as t → -∞ (4 + 6e^2t) / (5 - 9e^3t) → (4 + 6*0) / (5 - 9*0) = 4/5