How do you find the limit of ( e^(3t) - 1 ) / t as x approaches 0?

1 Answer
May 28, 2016

3

Explanation:

We will be using e^x= sum_{n=0}^{infty}x^n/(n!)
Taking e^{3t} = 1 + 3t+(3t)^2/2+(3t)^3/6+... and substituting
lim_{t->0}(e^{3t}-1)/t = lim_{t->0}((1+ 3t+(3t)^2/2+(3t)^3/6+...-1)/t)
lim_{t->0}(e^{3t}-1)/t =lim_{t->0}(t((3+(3t)/2+(3t)^2/6+...))/t)=3