# 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.

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

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

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