# Math Help - Understanding formal statement of L'hospital's Rule

1. ## 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 $\lim_{x\rightarrow a} f(x)/g(x)$= $\lim_{x\rightarrow a} f'(x)/g'(x)$

2. I'm trying to figure out what you're asking here....

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

3. 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.

4. delta is small so that means for all x's near this a, but x does not equal a since we have the >0

5. Can you post me the diagram so that I can visualise which will help me to understand the theory.