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Math Help - I have no clue how to solve this. (limit).

  1. #1
    Member integral's Avatar
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    I have no clue how to solve this. (limit).

    Find a value (a) such that:

    \lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4

    Any ideas?
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by integral View Post
    Find a value (a) such that:

    \lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4

    Any ideas?
    L'Hopital ...

    \displaystyle \lim_{x \to 0} \frac{a\sec^2(ax + \pi/4)}{1} = 4

    a = 2
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by integral View Post
    Find a value (a) such that:

    \lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4

    Any ideas?
    Evidently a\ne0. What if you let ax=y then x\to 0\implies y\to 0 so that our limit becomes \lim_{y\to 0}\frac{\tan(y+\frac{\pi}{4})-1}{\frac{y}{a}}=4\implies a=\frac{4}{\lim_{y\to0}\frac{\tan(y+\frac{\pi}{4})-1}{y}}. I'm sure you can deal with that limit.
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