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Infinit limit

  1. Jan 24, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]
    \frac{x}{x-5}
    [/tex]

    [tex]
    lim x\rightarrow\infty
    [/tex]


    2. The attempt at a solution


    [tex]
    \frac{x}{x-5} \equiv \frac{1}{1-\frac{5}{x}}
    [/tex]

    [tex]
    lim x\rightarrow\infty
    [/tex]

    how do i know what to plug into x to solve the problem. by the way it equals 1
     
  2. jcsd
  3. Jan 24, 2009 #2

    Mark44

    Staff: Mentor

    You don't have to plug anything into x. As x gets larger and larger, what does 1/(1 - 5/x) approach? Can you convince yourself that this expression gets closer and closer to 1 the larger x gets?
     
  4. Jan 24, 2009 #3
    so would you just plug zero for x and the simplify the problem which would give 1?
     
  5. Jan 24, 2009 #4

    jgens

    User Avatar
    Gold Member

    Perhaps to elaborate slightly on what Mark44 has posted: At this moment in time consider lim (x -> infinity) 1/x. We want to find what 1/x approaches as x becomes arbitrarily large. Let us first consider x = 10, then our expression becomes 1/10 = 0.1. Now suppose x = 100, then our expression becomes 1/100 = 0.01. Now suppose x = 100000, than our expression becomes 1/100000 = 0.00001, and for even larger x the expression becomes even smaller; hence, the limit aproaches 0.

    Edit: You would not let x = 0, you may let the expression 5/x approach zero as x tends to inifinity though.
     
  6. Jan 24, 2009 #5
    Thanks, that makes sense.
     
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