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Easy Calculus Problem

  1. May 11, 2004 #1
    Ok, I have 2 problems. I think my first one deals with an algebra II thing. But, it's: Evaluate the limit (if it exists):

    lim (x approaches -2) (x+2)/(x^3 +8)

    I think my problem came from factoring the denominator, which I got as
    (x+2)(x^2 - 4x +2), so my answer came out to be 1/14, which is not one of the answer choices. I can't remember factoring cubes. I know it's SOPSMS, but I can't even remember how to do that.

    My other problem. Can anyone give me an example of finding the gradient of a function at, say x=3, for something that has an exponent with a variable? Maybe 4^x. Thanks!!!!!!!
     
    Last edited: May 11, 2004
  2. jcsd
  3. May 11, 2004 #2
    You cube is almost correct but you needed to multiply 2 and x and have 2^2 at the end so you should get (x+2)(x^2 - 2x +4). The answer is 1/12
     
  4. May 12, 2004 #3

    NateTG

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    I assume you want, for example:
    [tex]\frac{d}{dx} 4^x=\ln 4 \times 4^x[/tex]

    (It's usually called a derivative in english. Gradient refers to other things.)
     
  5. May 13, 2004 #4

    HallsofIvy

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    In a bit more detail: if y= ax, then ln(y)= x ln(a) so (ln(y))'= (1/y)y'= ln(a)
    Then y'= ln(a) y= ln(a) ax.
     
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