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Homework Help: Please get me started on showing that the following limit exists

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Evaluate the limit or show it doesn't exist. (x→∞) lim ((x+2)/√x) where (x > 0)

    2. Relevant equations

    3. The attempt at a solution

    I know how to solve it if x → c but i don't know how to start it when it goes to infinity. I just need a hint as to how to start the problem.
  2. jcsd
  3. Mar 14, 2012 #2


    Staff: Mentor

    Divide each term in the numerator by √x, and then take the limit.
  4. Mar 14, 2012 #3
    Mark, thanks for responding,

    so after evaluating, i found that the limit does not exists... am i correct?
    ((x+2)/√x)/1 --- Does not exist since the numerator is always bigger than the denominator
    x→∞, x > o
  5. Mar 14, 2012 #4
    That's not what Mark meant. You essentially have the exact same equation you started with. Remember that

    [itex]\displaystyle\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}[/itex].
  6. Mar 14, 2012 #5


    Staff: Mentor

    In one sense, the limit doesn't exist, because (x + 2)/√x gets large without bound as x gets large. In that sense, the limit doesn't exist because it is not a finite number. For limits like this, though, we usually say that the limit is ∞.

    Also, because x is approaching infinity, you don't need to say that x > 0.
  7. Mar 15, 2012 #6
    So when x → ∞, a function will always either go to a finite number, ∞, or -∞...so will a function then always have a limit in this sense? Oh, nevermind, some functions can diverge, like f(x) = -1^x.
  8. Mar 15, 2012 #7


    Staff: Mentor

    Right, except that ##\lim_{x \to \infty}-1^x = -1##

    The one you're thinking of is f(x) = (-1)x. Without parentheses, what you wrote is the same as -(1x).
  9. Mar 15, 2012 #8
    Thank you. I think i understand now.
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