MATLAB: How to specify the assumption that a/v >> b for use with the LIMIT command in Symbolic Math Toolbox 5.1 (R2008b)

Symbolic Math Toolbox

I want to calculate the limit of f with
f = a/(b+(a/v))
If
 a/v >> b
then I expect the expression to approximate v. I could do something like:
limit(f,b,0)
but I would like to know if there is an ability to specify something like "a/v >> b" or "a/v – b >> 0".

Best Answer

The single assumption that a/v >> b is not sufficient for the expression f to approximate v.
For example, if
 a = 1, v = 1, b = -1e30
then f is approximately 1/b, and if
 a = 0
then f is 0.
Let us additionally assume that b > 0. With this additional assumption you could evaluate the expression as b/(a/v) approaches 0. To calculate this in MuPAD, we need to substitute the term
 b/(a/v)
with a new variable since LIMIT only accepts identifiers:
b = bva* a/v
Now, f can be expressed as:
 f = a/((a/v) + (a*bva)/v)
and you can evaluate the expression with:
limit(f, bva, 0)
If your interpretation of a/v >> b is something different it may be useful to actually look at how f changes for small values of b by observing the series expansion:
series(f, b)
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