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Finding limits/ derivative

  1. Sep 23, 2004 #1
    Would some one plz show me how to do these problems below.
    Thanks so much
    1) lim of n as n approaches to infinity 1/[1-(n/(n-1))]
    2) lim of n as n approaches to infinity (n-1)/[n-(1/n)]
    3) lim of n as n approaches to infinity n * sin (1/n)
    4) lim of n as n approaches to infinity (1/n)-(1/(n+1))

    ****Would u plz also explain this to me:
    Y does lim of x as x approaches to 0+ {[1+(x/2)]^(2/x)}^(1/2) = e^(1/2)???
    I dont understand y they r equal??
     
  2. jcsd
  3. Sep 23, 2004 #2
    Would some one plz show me how to do these problems below.
    Thanks so much
    1) lim of n as n approaches to infinity 1/[1-(n/(n-1))]
    2) lim of n as n approaches to infinity (n-1)/[n-(1/n)]
    3) lim of n as n approaches to infinity n * sin (1/n)
    4) lim of n as n approaches to infinity (1/n)-(1/(n+1))

    ****Would u plz also explain this to me:
    Y does lim of x as x approaches to 0+ {[1+(x/2)]^(2/x)}^(1/2) = e^(1/2)???
    I dont understand y they r equal??
     
  4. Sep 23, 2004 #3
    1) lim of n as n approaches to infinity 1/[1-(n/(n-1))]

    look at the n/n-1 part first.

    Times both the top and the bottom by 1/n. That gives you 1/(1-1/n) The 1/n term goes to zero, so this part = 1

    that leaves you with lim as x goes to 1 of 1/1-x, which is means the denominator goes to zero, so the equation goes to infinity.

    Why don't you post what part you are stuck on with the rest?
     
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