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Math Help - Quick question about limits and continuity

  1. #1
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    Quick question about limits and continuity

    Hey guys,

    So this is the problem
    Quick question about limits and continuity-exercises-46-48.png

    Simple question, in exercise 46 is this the correct way to do it?

    (f(x+h) - f(x))
    / h

    Or are they asking for some other way to do it? The answer I got was -0.4991 when using h = 0,001

    Anyone wanna help out?
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  2. #2
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    Re: Quick question about limits and continuity

    Rather than trying to identify them as derivatives, or use a calculator to estimate them, (or using L'Hopital) you should learn how to do them "directly". For each of those problems, the limit can evaluated directly if you first do some algebraic simplification. Problems like these represent a math technique/skill that you're expected to learn when you take calculus, the same way you're expected to learn various techniques for solving a quadratic equation (factoring, completeing the square, using the quadratic equation) in algebra 2.

    In each case here, simply, and then look for cancellation. Once you can algebraically cancel the troublesome denominator that's making it look like division by 0, you're golden.

    For 46, first make it a simple fraction, then eventually multiply by \frac{1+\sqrt{x}}{1+\sqrt{x}} to deal with the troublesome (1-\sqrt{x}) (that will show up after you simplify the entire fraction). Then look to cancel the denominator out (you'll be able to), and then you're virtually finished.

    For 47, again, first simplify it into a simple fraction, then look to cancel the denominator out (you'll be able to), and then you're virtually finished.

    For 48, expand out that (5+h)^2, simplify, then look to cancel the denominator out (you'll be able to), and then you're virtually finished.
    Last edited by johnsomeone; September 11th 2012 at 10:09 PM.
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