Question

Determine the right end-behavior of the function h(t)=3[(t+1)/t]^t


e3
0
3e
infinity

Answer 1

So what's happening for large values of t?\[\Large\bf\sf \lim_{t\to\infty}3\left(\frac{t+1}{t}\right)^t\]
Hmm

Answer 2

If you split up the fractions inside,
\[\Large\bf\sf \lim_{t\to\infty}3\left(1+\frac{1}{t}\right)^t\]You should be able to relate this to the limit definition of e.
Does it look familiar?