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Homework Help: Is this right?

  1. Mar 29, 2008 #1
    is this right??

    1. The problem statement, all variables and given/known data
    use the limit process to find the slope of the graph of the function at the specified point.

    f(x)= (sqroot of (x + 10)), at (-1, 3)


    2. Relevant equations
    f(a)= f(x) - f(a)/x-f(a)


    3. The attempt at a solution

    Lim as x-> -1 = sqrt of (x + 10) - sqrt of (-1 + 10)/ x- (-1)

    Lim as x-> -1 = sqrt of (x + 10) - sqrt of (9) / x - (-1)

    Lim as x-> -1 = sqrt of (x + 10) - 3 / x + 1

    thats as far as i could go...
    so is that the slope? or do i need to do nething further?
     
  2. jcsd
  3. Mar 29, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Do you mean "f'(a)= (f(x)-f(a))/(x- a)" here?


    Yes, you need to do something further! You haven't taken the limit yet.

    So far you have lim (x->-1) (sqrt(x+10)- 3)/(x+1) (Please use parentheses! It makes things much clearer!) Now, I would recommend "rationalizing the numerator": multiply both numerator and denominator by sqrt{x+ 10}+ 3. You should be able to cancel an "x+1" term in both numerator and denominator and then evaluate at x= -1.
     
  4. Mar 29, 2008 #3
    yes i did mean that...
    and thnx i think i got it now.. but just to check ..is this right?

    you have:
    lim (x -> -1) = (sqrt(x+10)-3)/(x + 1) • (sqrt(x+10)+3)/(sqrt(x+10)+3)

    then you have:

    lim (x -> -1) = ((x+10)-9)/(x+1)(sqrt(x+10)+3)

    (x+10)-9 simplifies to x+1 of course..then you can take the x+1's out of the numerator and denominator. then you get:

    1/(sqrt(x+10)+3)
    then when you put in the limit for x you get:

    1/(sqrt(-1+10)+3)
    1/(sqrt(9)+3
    1/3+3
    1/6

    that is the answer?
    [slope at (-1,3) is 1/6]
     
  5. Mar 29, 2008 #4
    When I differentiate that function, I get the same answer; so yes, it seems right.
     
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