Taking a limit inside a function and graphing it

Questions
,
1

Hello, thank you for your time.

I am trying to graph the following function:

f[x_] := 1/(Exp[(x-u)/(k*T)]+1);
Plot[f[x_],{x,0,1}]

I tried doing the above while setting T=0, but quickly learned that wouldn’t work. So I tried the following:

f[x_] := 1/(Limit[Exp[(x-u)/(k*T)],T->0]+1);

Then I tried to use the same plot. This gave me no errors but now unfortunately nothing is showing up on my graph. It should look like a step-function, where f(x) = 1 until x=u, then at that point f(x)=0 the rest of the way.

Any help is appreciated, thank you!

2

Need numerical values for u, k, T to plot a function of x. Possibly introduce ranges of values using Manipulate, In Plot, should have f not f. Sometimes missing plot region can be revealed by adding PlotRange->All.

3

Hi thanks for the response. I do have values for these constants. u=5, k=10^(-5), but T is approaching zero.

4 
In[1]:= u = 5;
k = 10^-5;
f[x_] := 1/(Limit[Exp[(x - u)/(k*T)], T -> 0] + 1);
Plot[f[x], {x, 0, 10}, AxesOrigin -> {0, -.1}]

Out[4]= ...PlotSnipped...
5

Bill, thank you so much for the sample! Maybe I am doing something wrong, but it is still not working. Here is the entirety of the code:

k=8.617*10^(-5);
In[1]:=u=5.49;
x=0;
f(x_):=1/(Limit[Exp[(x-u)/(k*T)],T->0]+1);
plot[f[x_],{x,0,10},AxesOrigin->{0,-.1}]

When I compile, nothing shows up on the graph

6

AHA got it! Its because I was using Plot[f]… I should have been using Plot[f]

Thanks everyone!

I do have one more question. What If I want to use

Manipulate[Plot[f(x)],{x,0,10},{T,0,300}]

Will this work? Because I am trying just that and it doesnt seem to be working

7

I actually got it working. I had to make f a function of x and T, like this:

f[x_,T_]...
Manipulate[Plot[f(x,T)......]