# Math Help - Taylor's series help on solving limits.

1. ## Taylor's series help on solving limits.

Hello everyone! I need some help with solving limits with Taylor's, I didn't really get the whole process yet.

I need to solve this guy:

Alright, I didn't really get where I am supposed to "stop" writing polinomials, my teacher said that I should stop when I find the smallest degree factor, because that's the one which is "bossing around" when the limit approaches zero.
Okay, that's where I've gone so far (see attachment)

I don't get if I wrote too many, if I didn't write enough terms, if I did something wrong at all, or I am right and should keep on doing calcs. Could someone help me out please? Thanks a lot!

2. ## Re: Taylor's series help on solving limits.

Originally Posted by dttah
Hello everyone! I need some help with solving limits with Taylor's, I didn't really get the whole process yet.

I need to solve this guy:

Alright, I didn't really get where I am supposed to "stop" writing polinomials, my teacher said that I should stop when I find the smallest degree factor, because that's the one which is "bossing around" when the limit approaches zero.
Okay, that's where I've gone so far (see attachment)

I don't get if I wrote too many, if I didn't write enough terms, if I did something wrong at all, or I am right and should keep on doing calcs. Could someone help me out please? Thanks a lot!
Everything looks great, just keep going!!!

first notice that the $x^2$ terms reduce out of the numerator. So now every term contains a factor of $x^4$

Now factor an x out of the parenthesis in the denominator to get

$x^2\cdot x^2 \cdot (2+x)^2$

Now reduce and take the limit as x goes to zero

3. ## Re: Taylor's series help on solving limits.

Ohhh *__* that's lovely.
Thanks a lot!
Just a little thing I don't get, when am I supposed to stop when doing such exercises? For example, looking now, I could have stopped at 4th degree.
My university teacher is very strict and she is the one who says "Doesn't matter if you can get to the result, it's important for you to do as few calcs as you can". And I would like to understand when am I supposed to stop writing polynomials... thank you!

4. ## Re: Taylor's series help on solving limits.

Originally Posted by dttah
Ohhh *__* that's lovely.
Thanks a lot!
Just a little thing I don't get, when am I supposed to stop when doing such exercises? For example, looking now, I could have stopped at 4th degree.
My university teacher is very strict and she is the one who says "Doesn't matter if you can get to the result, it's important for you to do as few calcs as you can". And I would like to understand when am I supposed to stop writing polynomials... thank you!
The idea is we needed to not have the denominator go to zero. So when I factored out the x that was the smallest power that would lead to a non zero denominator is we could reduce out all of the powers of x.

5. ## Re: Taylor's series help on solving limits.

Alright, I see. Thank you! You've been of GREAT help. Thanks a lot!