Hello from MrBillDoesMath!
Answer:
5
Discussion:
Consider the expansion of e^x:
e^x = 1 + x + x^2/2 + x^3/6 +...... => replace x by 5t
e^(5t) = 1 + (5t) + (5t)^2/2 + .... => subtract 1 from both sides
e^(5t) - 1 = (5t) + (5t)^2/2+.... => divide both sides by t
(e^(5t) -1)/ t = 5 + (25/2) t +....
so as t ends to 0 the quotient tends to
5 + (25/2)0 + (other terms) *0 -> 5
Thank you,
MrB
