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Math Help - tangent line equation of curve..

  1. #1
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    tangent line equation of curve..

    This is im sure very easy, but it was a busy summer. I am going through some questions early in my calc book, and im not sure of the best/easiest way to tackle this question. (please explain steps)

    The point P(2, ln 2) lies on the curve y = ln x. Using the point Q(2.001, ln 2.001) on the curve, a reasonable equation of the tangent line to the curve at P(2, ln 2) is?

    Cheers
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  2. #2
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    Quote Originally Posted by captain_jonno View Post
    This is im sure very easy, but it was a busy summer. I am going through some questions early in my calc book, and im not sure of the best/easiest way to tackle this question. (please explain steps)

    The point P(2, ln 2) lies on the curve y = ln x. Using the point Q(2.001, ln 2.001) on the curve, a reasonable equation of the tangent line to the curve at P(2, ln 2) is?

    Cheers

    I suppose that by "reasonable" they mean you calculate the equation of the line passing through the points P and Q . Use the folllowing, which is Junior H.S. stuff:

    ** Equation of the line passing through (x_1,y_1) and with slope equal to m : y-y_1=m(x-x_1)

    ** Slope of the line passing through the points (x_1,y_1)\,,\,(x_2,y_2)\,:\;\frac{y_2-y_1}{x_2-x_1} , unless x_1=x_2 and then the line passing through these points is a vertical one and its slope is undefined.

    Tonio
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  3. #3
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    Ok super, thanks.

    so y= x/2 -lnx +1 or what do you think
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    Quote Originally Posted by captain_jonno View Post
    Ok super, thanks.

    so y= x/2 -lnx +1 or what do you think

    m=\frac{\ln(2.001)-\ln 2}{2.001-2}\cong \frac{1}{2} , so the wanted line is:

     y - \ln 2=\frac{1}{2}(x-2)\Longrightarrow y = \frac{x}{2}+\ln 2 - 1

    Check your signs...

    Tonio
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    Thanks champ
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  6. #6
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    Quote Originally Posted by captain_jonno View Post
    Ok super, thanks.

    so y= x/2 -lnx +1 or what do you think
    y= x/2- ln x+ 1 can't possibly be correct because it contains "ln x" and so is not linear. Since the tangent line is at x= 2, you mean "ln 2".
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