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.

External Links

L'Hospital's Rule (Wolfram MathWorld)

Permanent Citation

Chris Boucher
​
​"L'Hospital's Rule for 0/0 Forms"​
​http://demonstrations.wolfram.com/LHospitalsRuleFor00Forms/​
​Wolfram Demonstrations Project​
​Published: August 25, 2008