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Math Help - limits

  1. #1
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    limits

    Consider the relationship involving g(x).

    8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

    Evaluate the following limit.

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  2. #2
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    Quote Originally Posted by zweevu View Post
    Consider the relationship involving g(x).

    8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

    Evaluate the following limit.

    This is a straightforward application of the sandwich theorem.

    Note that if

    8x \leq g(x) \leq 4x^4 - 4x^2 + 8 for all x, then

    \lim_{x \to 1}8x \leq \lim_{x \to 1}g(x) \leq \lim_{x \to 1}(4x^4 - 4x^2 + 8)

    8 \leq \lim_{x \to 1}g(x) \leq 8.


    What does this tell you about \lim_{x \to 1}g(x)?
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  3. #3
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    Quote Originally Posted by zweevu View Post
    Consider the relationship involving g(x).

    8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

    Evaluate the following limit.

    Since g(x) lies between the other two functions of x for all x, evaluate the limits of the others and analyze the result.
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