# L'Hospital's Rule for 0/0 Forms

L'Hospital's Rule for 0/0 Forms

One form of L'Hospital's rule states that if and as , then =. In this Demonstration, you can choose from a variety of functions with roots at 1 to form the numerator and denominator of a quotient. These functions are plotted as dashed curves and their quotient is plotted as a solid gold curve. The application of L'Hospital's rule to compute the limit of the quotient at 1 is shown above the plot.

f(x)→0

g(x)→0

x→a

lim

x→a

f(x)

g(x)

lim

x→a

f'(x)

g'(x)