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

  1. #1
    Newbie dttah's Avatar
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    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:
    Taylor's series help on solving limits.-4ecd4838e4b04e045aee647b-alfie-1322076258534-wolframalpha20111123132253954.gif


    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)

    Taylor's series help on solving limits.-salto.png


    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!
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Re: Taylor's series help on solving limits.

    Quote Originally Posted by dttah View Post
    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:
    Click image for larger version. 

Name:	4ecd4838e4b04e045aee647b-alfie-1322076258534-wolframalpha20111123132253954.gif 
Views:	28 
Size:	7.8 KB 
ID:	22864


    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)

    Click image for larger version. 

Name:	salto.PNG 
Views:	26 
Size:	3.8 KB 
ID:	22865


    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
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  3. #3
    Newbie dttah's Avatar
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    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!
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  4. #4
    Behold, the power of SARDINES!
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    Re: Taylor's series help on solving limits.

    Quote Originally Posted by dttah View Post
    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.
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  5. #5
    Newbie dttah's Avatar
    Joined
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    Re: Taylor's series help on solving limits.

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