SOLUTION: Which function dominates as x approaches infinity ? 5*2^x OR 69000x^18

f(x) is said to dominate over g(x) if 

  lim = 0
 x->

5*2x dominates because

 lim  = 0
x->

The reason we know this is because

1. This is a case of infinity over infinity , thus
   L'Hopital's rule applies.
2. Each derivative of the numerator up through the 17th will result
   in a non-zero constant times a power of x and will thus approach 
   infinity.
3. Each derivative of the denominator up through the 17th will result in a
   constant times 2x and will thus approach infinity.
4. Thus up through the 17th derivatives of the numerator and denominator
   the result will be a case of  and L'Hopital's rule will apply. 
5. The 18th derivative of the numerator will result in a constant
6. The 18th derivative of the denominator will still result in a constant
   times 2x which is a case of a constant over infinity
7. The limit of a constant over an expression that approaches infinity
   as x approaches infinity is zero. 
   
 lim  = 
x->
 
 lim  =
x->

13800 lim  =
     x->
... =

lim  = 0
      x->

Edwin