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LImits Question

  1. Dec 10, 2005 #1
    Good Day

    I have this limit question that I need to evaluate. I know the answer but am unsure how to answer it.

    Evalualte:

    lim (3^(x+1))(2-3^(-x))
    x-> -Infinity

    I know the answer is -3.

    Any help would be great
     
  2. jcsd
  3. Dec 10, 2005 #2
    have you tried it?
     
  4. Dec 10, 2005 #3
    try distrubuting the [itex] 3^{x+1} [/itex]
     
  5. Dec 10, 2005 #4
    just looking the my proofs solution I don't understand how 3^(x+1) * 2 = 2e^(x+1). Can anybody explain this?
     
  6. Dec 10, 2005 #5

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    No, because they aren't equal.
     
  7. Dec 10, 2005 #6
    i'm not sure what that is, but this is how i proved it:
    [tex] \lim_{x\rightarrow -\infty} 3^{x+1} (2-3^{-x}) [/tex]
    [tex] \lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3^{x+1-x} [/tex]
    [tex] \lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3 [/tex]
    where x approaches negative infinity, therefore, [itex]3^{-\infty} \rightarrow 0 [/itex]
    [tex] \lim_{x\rightarrow -\infty}3^{x+1} (2-3^{-x}) = - 3 [/tex]
     
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