Results 1 to 2 of 2

Thread: limit identity proofs

  1. #1
    Member Greengoblin's Avatar
    Joined
    Feb 2008
    From
    UK
    Posts
    182

    limit identity proofs

    I have these identities for limits:

    let, $\displaystyle \lim_{x\to a} f(x)=b\text{ }\lim_{x\to a} g(x)=c$

    then:

    $\displaystyle \textcircled1 \lim_{x\to a}kf(x)=kb\text{ for a fixed constant k}$

    $\displaystyle \textcircled2 \lim_{x\to a}[f(x)\pm g(x)]=\lim_{x\to a}f(x)\pm\lim_{x\to a}g(x)=b\pm c$

    $\displaystyle \textcircled3 \lim_{x\to a}[f(x)g(x)]=\lim_{x\to a}f(x)\lim_{x\to a}g(x)=bc$

    $\displaystyle \textcircled4 \lim_{x\to a}\left[\frac{f(x)}{g(x)}\right]=\frac{\lim_{x\to a}f(x)}{\lim_{x\to a}g(x)}=\frac{b}{c} \text{ } (c\ne 0)$

    $\displaystyle \textcircled5 \lim_{x\to a}[f(x)]^{\frac{1}{n}}=b^{\frac{1}{n}} \text{ if } [f(x)]^{\frac{1}{n}} \text{ and } b^{\frac{1}{n}} \text{ are real}$

    Apparently there is some rigorous way of proving these, but my book doesn't give them. Can someone give me some hints of what I need to do? Do I use the Epsilon-delta method msomehow?

    (please don't prove, I want to have a crack myself).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,002
    Thanks
    1
    Here is a nice one on the product of limits. Yes, you can use the epsilon-delta method to show them. If you want rigor, that would be the way to go.

    http://www.math.uchicago.edu/~ershov...oduct_rule.pdf
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. identity proofs
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jun 21st 2010, 07:46 PM
  2. Help with trig identity proofs
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Jan 30th 2010, 06:12 PM
  3. More Trig/Pre-Cal Identity Proofs
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: Feb 3rd 2009, 06:42 PM
  4. Limit Proofs (Sup and Inf)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Sep 19th 2008, 12:58 PM
  5. [SOLVED] [SOLVED] Trig Identity proofs
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jan 21st 2007, 06:39 AM

Search Tags


/mathhelpforum @mathhelpforum