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Calculating limits by subbing in values

  1. Sep 28, 2012 #1
    Doesn't solving limits by substituting values defeat the point? For example: you can solve a limit of a quadratic by just subbing in a x value. But how do we know limit as x approaches a is the same as f(a)?
     
  2. jcsd
  3. Sep 28, 2012 #2

    haruspex

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    Please clarify with an example.
     
  4. Sep 28, 2012 #3
    I'll try to take a stab at what you're getting at :)

    For limits, we are concerned what y-value the function is headed for. It doesn't matter if there is a hole or something at that point, because the limit never actually equals the value x is headed towards. It can get infinitely close, however.

    For some limits, we don't have to do much work or simplification. So, if you can plug in the x-value without the denominator being equal to 0, go for it!

    Also, if lim x-> a of f(x) exits and equals f(a) , we call the function continuous (Assuming f(a) exists as well)
     
  5. Sep 29, 2012 #4
    Never mind.

    My prof. answered my question in lecture today. It's called the direct substitution property.

    http://web.viu.ca/wattsv/math121/Overheads/section14/directsubstitution.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
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