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Thread: limitation problem

  1. #1 a limitaiton problem 
    Forum Freshman
    Join Date
    Jun 2005
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    14
    hello:
    may anybody help me with this in my practicing book.

    lim(ln(1+x)/x)=lim[(1/x)ln(1+x)] 1)
    =lim(ln(1+x)^(1/x)) 2)
    =ln(lim(1+x)^(1/x)) 3)
    =lne=1 4)
    (x->0)

    i don't understand how to derive 3) from 2) based on which principal or theorem.

    any comment is appreciated.


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  3. #2 limitation problem 
    Forum Freshman
    Join Date
    Jun 2005
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    14
    hello:
    may anybody help me with this:
    here is my problem:
    calculate:lim((1-4x)^((1-x)/x)) (x->0) 1)

    here is my process of solving it:
    1)=lim(1+(x/-(1/4)))^(-4/x)*(1+x/(-1/4))^(5/x-1)
    =e*lim(1+x/(-1/4))^(5/x-1)
    =e*lim(1+x/(-1/4))^lim(5/x-1)
    =e*1^(infinite big number)
    =e

    obvious even i myself know it is wrong.but how can i solve it


    any comment is appreciated.


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  4. #3 limitation problem 
    Forum Freshman
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    Jun 2005
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    limitation problem:
    hello:
    may anyone give me a hint on this
    i have to solve this based on two theorem of e:

    lim(1+x)^(1/x)=e (x->0)
    and lim(1+(1/x))^x=e (x->infinite big positive or small negative)

    the problem:
    the value of lim((1+x)/(1-x))^(1/x) (x->0)
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  5. #4  
    Forum Isotope (In)Sanity's Avatar
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    Oct 2004
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    Mesa AZ
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    Posts merged.
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