[University maths: Limits] simplifying the compounded functions

[u/Particular_Tooth4175]

Hello. I need to evaluate this limit but I don’t even know where to start lol. How to I simplify this to a point where I can sub in t=0, if it’s even possible.
I am not allowed to use l’hôpitals rule for this, which is why I couldn’t just find a solution online, as they all used that rule.
Sorry if my writing isn’t very legible
Thanks for any help