# L'Hospital Rule

1. Nov 17, 2009

### Slimsta

1. The problem statement, all variables and given/known data
http://img692.imageshack.us/img692/6661/36979008.jpg [Broken]

2. Relevant equations

3. The attempt at a solution
whats wrong with it? im 100% sure and i can explain each one!
the first one equals 3 right?

second one should be true cuz 0/0 can be any number.. (thats what my teacher from high school said at least)

Last edited by a moderator: May 4, 2017
2. Nov 17, 2009

### clamtrox

3. Nov 17, 2009

### Slimsta

yeah but i guess i think that i know everything but something might be wrong..
and it will take me a long time to write down an explanation for each one :/

is the 3rd one right? i mean, f/g has to be g cannot = 0.. but its not in the lhospital rule...

4. Nov 17, 2009

### Slimsta

5. Nov 17, 2009

### HallsofIvy

Staff Emeritus
What exactly is your question? In your first post you said "im 100% sure and i can explain each one!"

The only question I can find is in your second post, "is the 3rd one right? i mean, f/g has to be g cannot = 0.. but its not in the lhospital rule... " In order that we be able to use L'Hospital's rule directly, we must have $\lim_{x\to a} g'(x)\ne 0$ and that's impossible if g'(x)= 0 in some neighborhood of a. We might be able to extend L'Hopital's rule in the case that f'/g' goes to 0/0 itself by using L'Hopital's rule again, but in order for that to work eventually, there must be some nth derivative of g which has non-zero limit at x= a but again, that's impossible if there is some neighborhood of a in which g' is 0.

6. Nov 17, 2009

### Slimsta

my question is, which one from the picture above is wrong?

Last edited: Nov 18, 2009
7. Nov 18, 2009

### Slimsta

please someone!! i checked it over like 20 times now..
1. is 'false' for sure cuz it limit = 3
2. its a fact so 'true'
3. its a rule so 'true'
4. its part of the rule so 'true'
5. small number / big number = closer and closer to 0 ==> 0 so 'true'
6. limit of infinity = infinity.. :| so 'true'
7. like the 3rd one but in words, so 'true'

whats wrong with it??

8. Nov 18, 2009

### willem2

point 4. g'(x) must be nonzero in some interval that contains c. This should be:
in every interval that contains c, g'(x) can't be zero everywhere in that interval.

9. Nov 18, 2009

### jgens

I would reconsider number 6. Just think about what would happen if $\lim_{x \to \infty}f(x) = -\infty$.

10. Nov 19, 2009

### Slimsta

those are such small things that both me and 2 of my buddies didnt pick on.. oh man. :|

thanks guys