Limits and Derivatives and Ruby

I read this article about Lisp: http://funcall.blogspot.com/2009/03/not-lisp-again.html
I wanted to try doing the same in Ruby.
I didn't like his setting DX as a constant close to 0 to shortcut not creating a function to figure the limit.

lim=lambda{|f,h|
 y=h
 1.upto(1.0/0) {|p| ##to infinity
   x=h+(1.0/10)**p ##increase how close x is to h 1.0,0.1,0.001 etc..
   fx=f[x] ##get f(x)
   break if y==fx ##if we start getting the same val, stop
   y=fx ##store the last val
 }
 y ##return where we stopped
}
ddx=lambda {|f|
 lambda {|x|
  lim[lambda{|dx| ##the limit of the derivative function
   (f[x+dx]-f[x])/dx
  },0] #as h approaches 0
 }
}

Here are some results
(Infinite limits) http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Infinite-Limits.topicArticleId-39909,articleId-39873.html

irb(main):319:0> g=lambda{|x| 1/(x**2)}
=> #
irb(main):320:0> lim[g,0]
=> Infinity
irb(main):321:0> g=lambda{|x| (1/(x**2))-(1/(x**3))}
=> #
irb(main):322:0> lim[g,0]
=> -Infinity

Derivatives

irb(main):326:0> g=lambda{|x| x**3}
=> #
irb(main):327:0> ddx[g][2]
=> 12.0000009928844

I tried for hours to get the limit to resolve to a nice integer... but could never quite get it to be more precise. I did this because i googled "derivatives calculus ruby" and couldn't find anything about this. Why not?