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Math Help - Limit w/ Inequality and Domain - Need some help!

  1. #1
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    Limit w/ Inequality and Domain - Need some help!

    Hello all! Just joined this forum today so hopefully you guys can guide me towards the right answer!

    I'm in Calculus I right now and I am doing very well, but this problem has me a bit stumped. I tried applying the Sandwich Theorem but I can't figure out where to go from here!

    Here is what I have:



    Suppose that

    Find the limit of f(x) as x approaches 0.



    If I just substitute 0 for x, I get 1≤f(x)≤1, which would make the answer 1. Is that even remotely correct? Or am I making this WAY more complicated than it really is?

    Thanks in advance!
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  2. #2
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    In limit problems it is never correct to substitute.
    We say that as x approaches 0, 1-x^4 approaches 1.
    As x approaches 0, \sec(x) approaches 1.
    Therefore, as x approaches 0, f(x) approaches 1.
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  3. #3
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    Ah, so is the domain there to limit sec/cos to quadrants I and IV?

    Also, I understand that substitution normally does NOT work with limits, however my professor always says to quickly check in your head if substitution yields an indeterminate value before proceeding. Did you substitute values on either side of 0 to find the answer?
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