Evaluate the limit as y approaches 4

  1. 1. The problem statement, all variables and given/known data

    Evaluate lim y→4

    y-3√y + 2
    √y - 2



    3. The attempt at a solution

    If I plug 4 into Y, my answer is undefined. But if I do the chart method, where I plug in 3.999 and 4.0001 the answer is 1. So I'm not quite sure what I'm doing wrong.
     
  2. jcsd
  3. Try factoring the numerator! The square roots might throw you off a bit, but it's in the same form of a quadratic equation.

    You can't plug in 4 directly because the function isn't defined at 4. But limits don't concern themselves with what happens at that point, only what happens very close to that point.
     
  4. Mark44

    Staff: Mentor

    The numerator is quadratic in form, and can be factored.

    Or, you can let u = √y, and rewrite the fraction in terms of u, and factor the numerator. With this change, the limit will be as u → 2.
     
  5. Mark and Scurty, thank you. Mark I get your second method, but for both of you, I don't understand how to factor the numerator. Is it really factor-able? I dont get what value to factor by.
     
    Last edited: Mar 15, 2012
  6. SammyS

    SammyS 8,875
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Of course 4.001 & 3.999 won't give you exactly 1. They give 0.99975 and 1.00025 respectively.
     
  7. Can you use parenthesis? I can't tell what your sqrt is encompassing.
     
  8. Just the Y. Nothing else.
     
  9. Mark44

    Staff: Mentor

    Parentheses aren't needed. √y is just the square root of y.
     
  10. Can someone tell me how exactly do I factor the numerator?
     
  11. Mark44

    Staff: Mentor

    (√y - ?)(√y - ?)

    Like that...
     
  12. Mark44

    Staff: Mentor

    Or if you use my suggestion, you're factoring u2 - 3u + 2.
     
  13. I totally forgot factoring square roots. Thanks. Saved me alotta trouble.
     
    Last edited: Mar 15, 2012
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