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Math Help - Tangent Problems

  1. #1
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    Tangent Problems

    I would have put this in the same thread as my other ones, but I've been told that its better not to clutter up one thread with too many questions. Here are two more practice problems I was having trouble with.





    For this one, I'm not sure what I should do. It seems that I should be applying the Sum, Difference, and Constant Rules, but I'm not sure where I should begin with this one.

    For example, for (a), should I simply add f(x) + g(x) and plug in 2 for the x value?
    (6x+2) + (6x-2) = 12x = 24? I know thats probably wrong as it seems too easy to be the solution to the question.
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  2. #2
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    You have a mistake in the algebra.
    \dfrac{{\sqrt {11x + 11h}  - \sqrt {11x} }}<br />
{h} = \dfrac{{11h}}<br />
{{h\left( {\sqrt {11x + 11h}  + \sqrt {11x} } \right)}} = \dfrac{{11}}<br />
{{\left( {\sqrt {11x + 11h}  + \sqrt {11x} } \right)}}

    Now \displaystyle\lim _{h \to 0} \frac{{11}}<br />
{{\left( {\sqrt {11x + 11h}  + \sqrt {11x} } \right)}} = \frac{{11}}<br />
{{2\sqrt {11x} }}
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  3. #3
    MHF Contributor Unknown008's Avatar
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    For the second one, I'm not sure, but this is what I would do:

    y = f(x) + g(x)

    \dfrac{dy}{dx} = \dfrac{d}{dx}(f(x) + g(x))

    This gives:

    \dfrac{dy}{dx} = f'(x) + g'(x))

    \dfrac{dy}{dx} = 6+6 = 12

    (6 and 6 from the gradients of the tangents)

    Ok, now when x = 2, y1 = 14
    When x = 2, y2 = 10

    (Those y coordinates are from the equations of the two tangent equations)

    So, the y coordinate of f(x) + g(x) = 10 + 14 = 24

    (Add those y coordinates because when functions add, it's their y coordinates which add up)

    Hence, we get:

    \displaystyle \int^y_{24}\ dy = \int^x_2 12\ dx

    This gives: y - 24 = 12x - 24

    y = 12x
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  4. #4
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    @Unknown008;581689
    I think that if you are going to offer help you should consider the level of the question.
    This question is clearly a very basic almost pre-derivative question.
    Therefore, giving an answer involving derivatives let alone integrals is not helpful.
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  5. #5
    MHF Contributor Unknown008's Avatar
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    Quote Originally Posted by Plato View Post
    @Unknown008;581689
    I think that if you are going to offer help you should consider the level of the question.
    This question is clearly a very basic almost pre-derivative question.
    Therefore, giving an answer involving derivatives let alone integrals is not helpful.
    Yes, sorry... it's just that in my educational system, we were taught directly derivatives and integrals. The limits definition for example, was never taught to me. It's only a while ago that I learned a little more about it and how it worked. I'll be more careful next time.
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