Creating L'hopital's rule - WITHOUT the Limit command?

Hello, all.

For a recent assignment, I need to create a new function m-file - mylhopital(f,g,a) that will duplicate L'hopital's rule, only without any use of the LIMIT command. In this case, f and g are function handles, while a is the value that x approaches.

The assignment instructs me to calculate the limit of each case by writing a WHILE program that will replace f with f' and g with g' every time f(a) and g(a) equal 0, until f(a) and g(a) have taken on non-zero values.

What code I've written so far (with countless different permutations) is as follows:

   function j=mylhopital(f,g,a)
   syms x
   while (f(a)==0 && g(a)==0)
       f(a)=diff(f(x),x,a);
       g(a)=diff(g(x),x,a);
   end
   j=f(a)/g(a);
   end

I foolishly thought that this was fine, but it's only fine for samples of (f,g,a) that don't boil down to 0/0 in the first place. When I try to execute mylhopital(@(x)sin(x),@(x)x,0) or mylhopital(@(x)2-2*cos(3*x),@(x)x^2,0), the entire thing blows up and Matlab tells me that I have too many output arguments.

Answer 1

[Star Strider]

You don’t need symbolics.

Example:

mylhopital = @(f,g,a) (f(a+1E-8)-f(a)) ./ (g(a+1E-8)-g(a));

% sin(x)/x:
xf = @(x) x;
Lh1 = mylhopital(@(x)sin(x), xf, 0)

% 2-2*cos(3*x)/x^2
Lh2 = mylhopital(@(x)2-2*cos(3*x), @(x)x^2, 0)

produces:

Lh1 =

       1.0000e+000

Lh2 =

       8.8818e+000

[Chong]

Forgive me, Sir, but that's not quite I was asking.

Using symbolics was part of the assignment's requirements. Apart from that, I need the code to be in the format I posted up there. I appreciate you writing an entirely new one, but I was asking if anyone could repair mine.

[Star Strider]

I was suggesting a simpler way to approximate it.

The problem is that in calculating the derivatives, f and g lose their definitions as functions because they were not originally defined as symbolic functions. The solution is to use the subs function:

syms x
fa = f(a);
ga = g(a);
while (fa==0 && ga==0)
        f=diff(f,x);
        g=diff(g,x);
        fa = subs(f,x,a);
        ga = subs(g,x,a);
end
j=fa/ga;

This produces for the first set:

j =

1

and for the second:

j =

9

as expected.

That may not be the only way to do what you want, but it works!

[Chong]

Thank you so very much, Sir.

[Star Strider]

My pleasure!