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Tangent lines and natural logs homework help.

  1. Nov 16, 2007 #1
    1. The problem statement, all variables and given/known data
    1. Let f be the function defined by f(x) = -2 + ln(x^2).
    a) For what real numbers x is f defined
    b) Find the zeros of f
    c) Write an equation for the line tangent to the graph of f at x=1


    2. Relevant equations



    3. The attempt at a solution

    a) all positive reals except 0 ( i believe)
    b) Teacher lets us use calculator so : 2.718 , -2.718 (no hurt in checking that)
    c)at x = 1 , y = -2
    Finding slope/derivative:
    0+ (1/x^2)(2x)
    2x/(x^2)
    plug 1 in for the slope: 2(1) / (1)^2
    m= 2
    Equation: y+2 = 2(x-1) (i believe its correct but i'm not sure)
     
  2. jcsd
  3. Nov 16, 2007 #2

    rock.freak667

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    Homework Helper

    a) Should be correct as it is given in that form of ln(x^2)
    b) -2 +ln(x^2)=0
    ln(x^2)=2
    x^2=e^2

    I think you forgot to take the sq. root after

    c) Correct
     
  4. Nov 17, 2007 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Being allowed to use a calculator doesn't mean you are required to! No, 2.718 and -2.718 are NOT zeros of f. e and -e are. Do you understand the difference?
    Oh, and whether your teacher requires it or not you should always show HOW you solve a problem, not just give the answer.

    Are you serious? You actually put x= 1 into 2x/x^2? 2x/x^2= 2/x obviously. In fact, the whole problem is simpler if you write f(x)= -2+ ln(x^2)= -2+ 2ln(x). Then f' (x)= 2/x.
     
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