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Thread: Using formal definition of a limit

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    Question Using formal definition of a limit

    Can someone help me complete the derivative computation below? I'm a bit stuck.

    Using formal definition of a limit-img_20190615_161557.jpg
    Last edited by otownsend; Jun 15th 2019 at 12:17 PM.
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    Re: Using formal definition of a limit

    Quote Originally Posted by otownsend View Post
    Can someone help me complete the derivative computation below? I'm a bit stuck.

    Click image for larger version. 

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    Your last 3 steps should not have the limit statement in front of them because you already took the limit. The next to last step to the last step is wrong:
    $\frac{4-2a}{2-a} = \frac{2(2-a)}{2-a} = 2$
    It would be much better for you to type the equations so we could edit your post.
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    Re: Using formal definition of a limit

    $g(x)=2x-1$

    derivative of $g$ at any value $x=a$ in the domain of $g$

    $\displaystyle g(a) = \lim_{x \to a} \dfrac{g(x)-g(a)}{x-a}$

    $\displaystyle g(a) = \lim_{x \to a} \dfrac{2x-1 - (2a-1)}{x-a}$

    $\displaystyle g(a) = \lim_{x \to a} \dfrac{2x-2a}{x-a}$

    $\displaystyle g(a) = \lim_{x \to a} \dfrac{2(x-a)}{x-a}$


    $\displaystyle g(a) = \lim_{x \to a} \dfrac{2( \cancel {x-a})}{\cancel {x-a}} = 2$
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