Quandaries
and Queries 

Find the limit of [(1/(x+4))(1/4)]/x as x approaches zero. How do you use l"hopital's rule to find this limit. I know how to do it with multiplying everything by 4(x+4), and getting the answer, 1/16.But how do you apply derivatives with l'hopitals rule to this type of problem? 

Hi Abraham, I would do this problem the way you did, but if you insist on using l'hopital's rule you can do so. As x approaches zero both the numerator
and the denominator
approach zero, so it is valid to apply l'hopital's rule. The derivative of the numerator (using the quotient rule) is
and the derivative of the deminator is 1, so one application of l'hopital's give the limit, as x approaches zero, of
This limit is clearly ^{1}/_{16}, so the value of the original limit is ^{1}/_{16} also. Penny 

