Limit of a two variable function, assuming one is constant

Questions
1

Hi everyone,

I am quite new to Mathematica and I am stuck with something that I believe is not supposed to be that hard.
I have the following function defined:

a[f_,d_] := f (1 - Exp[-d f])

I want to find the limit of a when d → Infinity assuming f is a constant greater than 0.
I tried:

Limit[a[f,d]/;f>0,d->Infinity]

But it fails at providing f as the answer.

I must be doing something wrong. Can anyone help me?

Thanks.

Yohann

2

Hi Yohann,

When you are defining a function, the arguments have to be patterns. So, try this:

a[f_, d_] := f (1 - E^(-d f))

Then look at the help for Limit. Some searching will reveal the use of Assumptions.

In[5]:= Limit[a[f,d],d->Infinity,Assumptions->f>0]
Out[5]= f

Eric

3

Hi Eric,

I had the pattern declaration, it’s too bad I did not spot it when I proof-read my question.
What I was missing though, was the `Assumptions->f>0’ option to the Limit function.

You are right in suggesting that the documentation should have helped me. As you probably noticed, I was trying to implement the assumption in the function definition and did not think to look around the Limit options. I guess when you get to know a tool better, you also improve at searching for documentation.

Anyway, thank you for your time and for your answer.

Yohann