Could you remind what an indeterminate form is?
And what if f(x) = g(x)?
And what if a = 0, f(x) = x and p(x) = 1/x?
The bigger the denominator, the bigger the ratio?
And what if p(x) = q(x)?
I have such a problem:
Given that lim x->a f(x) = 0, lim x->a g(x) = 0, lim x->a h(x) = 1, lim x->a p(x) = INF, lim x->a q(x) = INF,
Evaluate these limits:
- Lim x->a f(x)/g(x) =
- Lim x->a f(x)/p(x) =
- Lim x->a h(x)/p(x) =
- Lim x->a p(x)/f(x) =
- Lim x->a p(x)/q(x) =
I have to mention which of these limits are indeterminate forms, positive INF, Negative INF, or the limit does not exist (DNE) or we don’t have enough info to determine the limit.
- Lim x->a f(x)/g(x) = 0/0, (DNE)
- Lim x->a f(x)/p(x) = 0/INF, (Indeterminate form)
- Lim x->a h(x)/p(x) = 1/INF, (positive infinitive)
- Lim x->a p(x)/f(x) = INF/0, (Indeterminate form)
- Lim x->a p(x)/q(x) = INF/INF, (DNE)
I'm not quite sure in my reasoning so I need your input, thanks
Could you remind what an indeterminate form is?
And what if f(x) = g(x)?
And what if a = 0, f(x) = x and p(x) = 1/x?
The bigger the denominator, the bigger the ratio?
And what if p(x) = q(x)?
it is a result that doesn't provide enough info about the actual limit after replacing the values in the expression,
so, wait a min, if by indeterminate forms is meant 0, 0/0, inf, inf/inf, it means I have some more indeterminate forms in my problem?
you mean what if 0 = 0, ? but this is also an indeterminate form, isn't it?
then f(x)=0 and p(x)=1/0 and are indeterminate forms
well, actually, the bigger the denominator, more the values of f(x) approaches 0 (from how I understood, lesser and lesser parts of 1 we obtain, e.g. 0,5; 0,001; 0,00001 and so on)
but this means that INF = INF
=> indeterminate forms, too?
Look I know that I am not as nice an instructor as emakarov.
But I must tell you that I think that you have all of these concepts confused.
Lets look at #2,
You have a fraction. Its numerator is very 'close' to 0.
Its denominator is very large in a positive sense.
Here is an example: .
Of what do you think that fraction is approximation ?
Now you have correctly listed Indeterminate forms, of which #2 is none of.
So can you repost this so that it makes sense?
If I were to have such an example I would write it as [1/10^100]/[10^100] = [1/10^100]*[1/10^100]... so, the limit DNE
if the lim x->a f(x) approaches o and lim x->a p(x) approaches INF =>the lim DNE
1. Lim x->a f(x)/g(x) = 0/0, (Indeterminate form)
2. Lim x->a f(x)/p(x) = 0/INF, (DNE)
3. Lim x->a h(x)/p(x) = 1/INF, (Indeterminate form)
4. Lim x->a p(x)/f(x) = INF/0, (Indeterminate form)
5. Lim x->a p(x)/q(x) = INF/INF, (Indeterminate form)
am I right (bc I feel I'm going to be more confused... )
ps: don't worry about the niceness while giving me advices, I appreciate much more the advices, not the way they are given
It truly troubles me that you are seemingly in a calculus course but know so very little about limits.
Please study this page on indeterminate forms.
LEARN all of those forms. Then complete rework what you posted, because most of your answers are completely wrong.
Thanks Plato, I got them:
1. Lim x->a f(x)/g(x) = 0/0, (Indeterminate form)
2. Lim x->a f(x)/p(x) = 0/INF = 0 bc as f(x) approaches 0, p(x) becomes large
3. Lim x->a h(x)/p(x) = 1/INF = 0 since when h(x) approaches a finite nr p(x) becomes large
4. Lim x->a p(x)/f(x) = INF/0, DNE (I think we would need to evaluate limit from the right and from the left in order to be able to determine the lim)
5. Lim x->a p(x)/q(x) = INF/INF, (Indeterminate form)
The only remark is the following.
I am not sure if INF is included in DNE or not. The limit can be or it may not exist. The former happens when f(x) does not change sign in some neighborhood of a, and the latter happens when there are both positive and negative values f(x) when x is arbitrarily close to a: then p(x) / f(x) changes sign as x tends to a while its absolute value continues to grow.
When you say that the answer is c), it means that the limit does not exists for all function p(x) and f(x) under given assumptions. And this is not true: for some p(x) and f(x), the limit is +∞ or -∞. Therefore, I think the correct answer is that there is not enough information.
Frankly I am confused at this point, myself.
In the OP we are given that .
We are also told that "c) DNE or don't have enough information to evaluate it" Also "I have to mention which of these limits are indeterminate forms, positive INF, Negative INF, or the limit does not exist (DNE) or we don’t have enough info to determine the limit[I]."
I did not think that "that there is not enough information" was an option.
the confusing statement is that for c) the both answers are mentioned (1)DNE or 2) not enough info); therefore, whether I consider the situation 1) or 2), I have to chose the same c) answer,
sorry, but that's how the options were stated, and I checked the answers - it was c) the correct answer