# Understanding formal statement of L'hospital's Rule

• April 12th 2009, 10:13 PM
roshanhero
Understanding formal statement of L'hospital's Rule
The Statement of L'hospital's Rule given on my book goes like this-
"Let f and g be two real valued functions differentiable at each point x in $(a-\delta,a+\delta),$and g'(x) is not equal to 0 for all x such that $
0<\mid x-a\mid <\delta
$
.

If $\lim_{x\rightarrow a} f'(x)/g'(x)$exists and $\lim_{x\rightarrow a} f(x)=0=\lim_{x\rightarrow a} g(x)$,then $\lim_{x\rightarrow a} f(x)/g(x)$ also exists and $\lim_{x\rightarrow a} f(x)/g(x)$= $\lim_{x\rightarrow a} f'(x)/g'(x)$
• April 12th 2009, 10:19 PM
matheagle
I'm trying to figure out what you're asking here....

Quote:

Originally Posted by roshanhero
The Statement of L'hospital's Rule given on my book goes like this-
"Let f and g be two real valued functions differentiable at each point x in $(a-\delta ,a+\delta )$and g'(x) is not equal to 0 for all x such that $0<\mid x-a\mid <\delta$.
If

• April 12th 2009, 10:54 PM
Prove It
• April 13th 2009, 09:06 PM
roshanhero
I just could not understand the conditions given there for the L'hospital rule to apply i.e. the one given in the modulus sign.
• April 13th 2009, 09:35 PM
matheagle
delta is small so that means for all x's near this a, but x does not equal a since we have the >0
• April 14th 2009, 10:25 PM
roshanhero
Can you post me the diagram so that I can visualise which will help me to understand the theory.