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Homework Help: Limit Need someone to check

  1. Jan 11, 2010 #1
    1. The problem statement, all variables and given/known data
    http://img23.imageshack.us/img23/9366/95631341.jpg [Broken]

    http://img341.imageshack.us/img341/3416/37907619.jpg [Broken]
    lim f(x)
    x->[tex]1\infty[/tex]
    I don't know how to do the first one..
    ty!
    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 11, 2010 #2

    Mark44

    Staff: Mentor

    For the first problem, a through d and g are right, but e and f are wrong. The limit as x --> -1 is 1, not 3. Since both the left-side and right-side limits exist and are equal, the limit itself exists. It just happens that f(-1) is not equal to 1. That says that f is not continuous at x = -1.
     
  4. Jan 11, 2010 #3
    I think i got it
    just 1 more question,
    lim (1.01+(1/n))n
    x->[tex]\infty[/tex]
    How would you solve it?
     
    Last edited: Jan 11, 2010
  5. Jan 11, 2010 #4

    Mark44

    Staff: Mentor

    I think you mean as n --> infinity.
    As n gets larger, 1.01 + 1/n approaches 1.01. When the quantity 1.01 + 1/n is raised to the power n, what happens to the whole expression?

    Note that a similar limit, (1 + 1/n)^n has a quite different, and somewhat surprising limit value.
     
  6. Jan 11, 2010 #5
    Is it infinity?
    but when i put it in wolfram
    the left side limit is 0? I don't get it... Does it mean, the limit does not exist?
     
  7. Jan 15, 2010 #6

    Mark44

    Staff: Mentor

    Yes (1.01 + 1/n)n approaches [itex]\infty[/itex] as n approaches [itex]\infty[/itex]. I don't know what you're saying in regard to the left side limit -- n can approach [itex]\infty[/itex] only from one side. What are you asking?
     
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