Results 1 to 4 of 4

Thread: Limits

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    4

    Limits

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

    $\displaystyle \lim_{x\rightarrow{c}}{\frac{1}{x^3}} = \frac{1}{c^3} $
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    You need to give a formula for delta. It will depend on epsilon and c.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    4

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

    QUESTION
    Prove the following limit of a function using the (above) definition where
    c > 0
    $\displaystyle \lim_{x \rightarrow{c}}{\frac{1}{x^3}} = \frac{1}{c^3}$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using limits to find other limits
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Sep 18th 2009, 05:34 PM
  2. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Apr 26th 2009, 01:45 PM
  3. HELP on LIMITS
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Sep 23rd 2008, 11:17 PM
  4. Limits
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Sep 21st 2008, 10:52 PM
  5. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 25th 2008, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum