# L'Hospital Rule

## Homework Statement

http://img692.imageshack.us/img692/6661/36979008.jpg [Broken]

## 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)

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whats wrong with it? im 100% sure and i can explain each one!

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...

HallsofIvy
Homework Helper
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.

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.

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

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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??

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.

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

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

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

thanks guys