Trouble with rules

Questions
1

Hi all,

I am new to mathematica and am trying to get a hang of rules. Here is what I am trying to do.

I wanted to show in Mathematica that the Limit of

\begin{align*} \lim_{R \to \infty } \frac{e^{a R}}{e^R} = 0 & & | a | < 1 \end{align*}

So what I tried in Mathematica is Limit[ Exp[a*R] / Exp[R], R → [Infinity]].
But I don’t know how to force it use a rule like this: Abs[a]<1

Anyone know what would be the proper syntax in Mathematica to do the above?

Thanks in advance.

2

In[2]:= Limit[Exp[a*r]/Exp[r], r → [Infinity],
Assumptions → {Abs[a] < 1}]

Out[2]= 0
3

One thing to be aware of is that in Mathematica, when one mentions “rules” one is typically referring to things with head Rule or a List thereof. What you are dealing with in this case is assumptions.

I realize this is just nomenclature and not in general a big deal. But it is helpful to have the right terminology in the subject header since, for many people, that can determine what gets read.