L'Hospital's Rule for 0/0 Forms

f(x)

x-1

2

x

-1

3

x

-1

ln(x)

ln(1/x)

sin(x-1)

g(x)

x-1

2

x

-1

3

x

-1

ln(x)

ln(1/x)

sin(x-1)

One form of L'Hospital's rule states that if

f(x)→0

and

g(x)→0

as

x→a

, then

lim

x→a

f(x)

g(x)

=

lim

x→a

f'(x)

g'(x)

. 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.