How to make a loop until a function has a nonzero limit?

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Andy
Andy 2012-10-14
I'm making an application for L'hopitals rule so the condition has to be until one of the functions has derived enough to have a nonzero limit. For this application, I have to use a while loop so here's what I got already.
while (limit(f,x,0)==0 limit(g,x,0)==0)
a=diff(f(x));
b=diff(g(x));
end;
y=(limit(f,x,0))/(limit(g,x,0))
My problem is since I need to assign variables to differentiate the two functions and the variables cannot be the same as the ones I assigned to the functions, how can I tell the while loop to continue to derive the functions when the derived functions has a different variable?

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回答（2 个）

Matt J
Matt J 2012-10-14
If you're just trying to avoid overwriting f and g, why not just make prior copies of them:
a=f;
b=g;
while (limit(a,x,0)==0 limit(b,x,0)==0)
a=diff(a(x));
b=diff(b(x));
end;
y=(limit(a,x,0))/(limit(b,x,0))
Star Strider
Star Strider 2012-10-14
编辑：Star Strider 2012-10-14
I am not certain I completely understand your problem, but if you want to continue to differentiate your functions until you get a finite result, I suggest this approach:
syms a b c d f g x
f(x) = sin(x)
g(x) = 1 - exp(x)
c = f(x)
d = g(x)
k1 = 1;
while (limit(c,x,0)==0) && (limit(d,x,0)==0)
a=diff(c(k1,:));
b=diff(d(k1,:));
k1 = k1 + 1
c(k1,:) = a
d(k1,:) = b
end;
y = (limit(c(k1,:),x,0))/(limit(d(k1,:),x,0))
Vectors c and d store the intermediate results, so you do not overwrite your original functions.
  2 个评论
Andy
Andy 2012-10-14
I forgot to mention but the f and g in this function are function handles
Star Strider
Star Strider 2012-10-14
编辑：Star Strider 2012-10-14
I could only get this to work in the Symbolic Math Toolbox. I assumed that when you referred to limit in your code snippet, you were using it.
I just now tried the code I posted with f and g redefined as:
f = @(x) sin(x)
g = @(x) cos(x) - exp(x)
and it worked just as well as with the original function definitions.
NOTE: I'm using 2012b.

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