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Thread: Secant limit

  1. #1
    No one in Particular VonNemo19's Avatar
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    Secant limit

    How do I go about proving that $\lim_{x\rightarrow1/2}{2x\sec(πx)}=\infty$ with some type of rigor? I'm rusty.
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  2. #2
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    Re: Secant limit

    You are talking about the left handed limit \lim_{x \to \frac12^-} \frac{2x}{\cos \pi x}=+\infty
    Because \cos \tfrac\pi2 =0, \, 1 \ne 0 and \cos \pi x > 0, \, 2x > 0 for 0 < x < \tfrac12.
    Last edited by Archie; Jun 3rd 2017 at 12:03 PM.
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  3. #3
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    Re: Secant limit

    Prove that for every $\varepsilon>0$ there exists $\delta>0$ such that $x\in \left(\dfrac{1}{2}-\delta,\dfrac{1}{2}\right)$, you have $2x\sec(\pi x)>\varepsilon$
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