I need to prove the following statement

lim

x---> Infinity

3x^5-5logex/5e^x-2x^5

I have

logex/x^5 --> 0 as x---> Infinity

not sure about the other bit.

Also need to prove the following

lim

x--->o

x^2/1-e^x2 = -1

Can anyone help?

Printable View

- Jul 27th 2011, 09:32 AMArronProving Limits
I need to prove the following statement

lim

x---> Infinity

3x^5-5logex/5e^x-2x^5

I have

logex/x^5 --> 0 as x---> Infinity

not sure about the other bit.

Also need to prove the following

lim

x--->o

x^2/1-e^x2 = -1

Can anyone help? - Jul 27th 2011, 09:49 AMTKHunnyRe: Proving Limits
Almost impossible to make any sense of that. Please remember, if nothing else, that the Order of Operations still works.

These are very different animals:

x^2 / 1 - e^x2

and

x^2 / (1 - e^x2)

Also, what does "e^x2" mean? Maybe ? Or something else? - Jul 27th 2011, 09:50 AMchisigmaRe: Proving Limits
Try to multiply top and bottom by and observe what it happens... and also try to learn latex and observe what it happens (Itwasntme)...

Kind regards

- Jul 27th 2011, 11:54 AMArronRe: Proving Limits
Thanks. I have a problem with advance settings, I can get the characters up to place them in the tex. Can anyone help?

- Jul 27th 2011, 11:56 AMArronRe: Proving Limits
Sorry I do mean e^x^2 and without the brackets.

- Jul 27th 2011, 01:37 PMSironRe: Proving Limits
You have to calculate:

By using l'Hopital's rule we get:

- Jul 27th 2011, 01:50 PMSironRe: Proving Limits
The first limit:

Can we assume is the natural logarithm?

(I'm not from the USA, so I don't know if they mean the natural logaritm or the logarithm with base 10, because I always use for the natural logarithm) - Jul 27th 2011, 02:00 PMArronRe: Proving Limits
yes.

- Jul 27th 2011, 02:04 PMSironRe: Proving Limits
Ok, maybe it can be useful to wright:

- Jul 27th 2011, 02:09 PMArronRe: Proving Limits
ok, but how do we get to the limit = 0

- Jul 27th 2011, 03:57 PMmr fantasticRe: Proving Limits
- Jul 30th 2011, 09:09 AMSironRe: Proving Limits
To prove that:

My solution would be:

In general:

And so:

We can calculate now the two limits by using l'Hopitals rule:

So that means we get: