How to assign predetermined values for points of discontinuity

Does anyone know how I would be able to assign a pretermined value for a point of discontinuity? I am currently working on writing a script to determine values at cetrain points of v, and with the exception of v=10, the script is working just fine. at v=10, we are left with the indeterminate of 0/0. Using basic calculus and applying L'Hopital's rule, we can determine that at v=10, the output is .1. However, I don't know how to add this to my script, and am still getting the output of NaN. Any help on how to fix this would be appreciated.

v = 0:5:50
a_n=(0.01.*(10-v))./(exp((10-v)./10)-1)
b_n= exp(-v./80)./8
if v == 10
    then a_n = 0.1
end

Answer 1

[Matt J]

v0 = 10+(-3:0.01:3)*1e-8;

v=v0;
a_n=(0.01.*(10-v))./expm1((10-v)./10);

idx=abs(v-10)<1e-8;
v=v(idx);
a_n(idx)=(0.01)./(0.1+(10-v)./200);  %use Taylor approx
plot(v0,a_n,'x')

Answer 2

[Walter Roberson]

v = 0:5:50
a_n=(0.01.*(10-v))./(exp((10-v)./10)-1)
b_n= exp(-v./80)./8
a_n(v == 10) = 0.1;

Answer 3

[Steven Lord]

v = 0:5:50

v = 1×11

0 5 10 15 20 25 30 35 40 45 50

a_n=(0.01.*(10-v))./(exp((10-v)./10)-1)

a_n = 1×11

0.0582 0.0771 NaN 0.1271 0.1582 0.1931 0.2313 0.2724 0.3157 0.3609 0.4075

a_n = fillmissing(a_n, 'constant', 0.1) % Fill missing values (NaN) in a_n with a constant 0.1

a_n = 1×11

0.0582 0.0771 0.1000 0.1271 0.1582 0.1931 0.2313 0.2724 0.3157 0.3609 0.4075

b_n= exp(-v./80)./8

b_n = 1×11

0.1250 0.1174 0.1103 0.1036 0.0974 0.0915 0.0859 0.0807 0.0758 0.0712 0.0669