Simple question about symbolic limits
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Hello,
I am checking results derived by hand in a MATLAB (2019a) live script and have encountered the following problem (MWE below): When I try to take the limit of the expression
as (symbolic) variable l approaches 0, restricting
, MATLAB cannot find the limit I obtain by hand. However, when I choose arbitrary values for
instead of using an assumption, I get the same limit I derived by hand (which is independent of c). I suspect there is an obvious explanation for this that I am overlooking.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/313088/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/313091/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/313091/image.png)
MWE:
%Declare symbolic variables:
syms l real;
syms t real; assumeAlso(t>1);
syms a real; assumeAlso(0<a<1);
syms p real; assumeAlso(0<p<1);
syms e real; assumeAlso(e>0);
syms c real; assumeAlso(c>0);
syms w real; assumeAlso(0<w<1);
%Functions:
phi = e/(1+c)*l^(1+c);
z = t/l*(1-exp(-l/t));
n = p*(1+c)/(p*(1+c)+z*l/phi*w);
pn = t*p*(1-n)*exp(-l/t)/n*(1-exp(-1*(t*p*(1-n)*exp(-l/t)/(a*n))^(-1)));
%Limits:
limit(pn,l,0,'right')
MATLAB cannot reduce this limit. However, when I instead impose, e.g.,
, via
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/313097/image.png)
syms l real;
syms t real; assumeAlso(t>1);
syms a real; assumeAlso(0<a<1);
syms p real; assumeAlso(0<p<1);
syms e real; assumeAlso(e>0);
syms c real; assumeAlso(c>0);
syms w real; assumeAlso(0<w<1);
%Functions:
phi = e/(1+0.1)*l^(1+0.1);
z = t/l*(1-exp(-l/t));
n = p*(1+0.1)/(p*(1+0.1)+z*l/phi*w);
pn = t*p*(1-n)*exp(-l/t)/n*(1-exp(-1*(t*p*(1-n)*exp(-l/t)/(a*n))^(-1)));
%Limits:
limit(pn,l,0,'right')
I get the result I derived by hand. The same holds for seemingly all other positive values of c. Any idea what I'm overlooking?
Thanks in advance.
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Answers (1)
Ayush Gupta
on 12 Jun 2020
The limit specified is also dependent on c if c does not have small values. For small values of c, a simplified expression is yielded. Refer to the following link to know more about limit:
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