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Math Help - Limits

  1. #1
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    Limits

    Prove the following limit of a function using the definition of a limit (where c>0)

    \lim_{x\rightarrow{c}}{\frac{1}{x^3}} = \frac{1}{c^3}
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  2. #2
    Senior Member Tinyboss's Avatar
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    You need to give a formula for delta. It will depend on epsilon and c.
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  3. #3
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    Proving the limit of a function

    In response to the reply,no formula for delta depending on epsilon or c was given.For completeness sake,i will state the definition.

    DEFINITION
    Let A \subseteq \mathbb{R}, and let c be a cluster point of A. For a function f : A \rightarrow{\mathbb{R}}, a real number L is said to be a limit of f at c if, given any \epsilon > 0 there exists a \delta > 0 such that if x \in A and 0 < \mid x - c \mid < \delta then \mid f(x) - L \mid < \epsilon.

    QUESTION
    Prove the following limit of a function using the (above) definition where
    c > 0
    \lim_{x \rightarrow{c}}{\frac{1}{x^3}} = \frac{1}{c^3}
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  4. #4
    Senior Member Tinyboss's Avatar
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    You need to find a formula for delta, depending on epsilon and c, such that the above definition will be satisfied for any epsilon>0 and any c>0.
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