Results 1 to 5 of 5

Thread: prove a limit

  1. #1
    Banned
    Joined
    Jul 2009
    Posts
    107

    prove a limit

    Suppose that ;

    1)$\displaystyle f: R\rightarrow R^2$ such that : $\displaystyle f(x) =(sinx,cosx)$

    2)The Euclidian norm of a vector $\displaystyle v=(u_{1}, u_{2})$ is defined as :

    $\displaystyle ||v||_{Eu} =\sqrt{ u_{1}^2 +u_{2}^2}$

    3) The maxnorm of a vector $\displaystyle v=(u_{1},u_{2})$ is defined as :

    $\displaystyle ||v||_{max} = max( |u_{1}|,|u_{2}|)$

    Where $\displaystyle u_{1},u_{2}$ belong to the real Nos R

    Then prove :

    $\displaystyle \lim_{x\to 0} f(x) = (0,1)$ ,with respect to both norms

    I know that i have to prove the following:


    1) given ε>0 ,i got to find a δ>0 ,such that :

    if 0<|x|<δ , then $\displaystyle ||(sinx,cosx)-(0,1)||_{Eu}<\epsilon$

    2)given ε>0 ,i must find a δ>0 ,such that:

    if 0<|x|<δ ,then $\displaystyle ||(sinx,cosx)-(0,1)||_{max}<\epsilon$ .

    Any suggestions for that delta??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by alexandros View Post
    Suppose that ;

    1)$\displaystyle f: R\rightarrow R^2$ such that : $\displaystyle f(x) =(sinx,cosx)$

    2)The Euclidian norm of a vector $\displaystyle v=(u_{1}, u_{2})$ is defined as :

    $\displaystyle ||v||_{Eu} =\sqrt{ u_{1}^2 +u_{2}^2}$

    3) The maxnorm of a vector $\displaystyle v=(u_{1},u_{2})$ is defined as :

    $\displaystyle ||v||_{max} = max( |u_{1}|,|u_{2}|)$

    Where $\displaystyle u_{1},u_{2}$ belong to the real Nos R

    Then prove :

    $\displaystyle \lim_{x\to 0} f(x) = (0,1)$ ,with respect to both norms

    I know that i have to prove the following:


    1) given ε>0 ,i got to find a δ>0 ,such that :

    if 0<|x|<δ , then $\displaystyle ||(sinx,cosx)-(0,1)||_{Eu}<\epsilon$

    2)given ε>0 ,i must find a δ>0 ,such that:

    if 0<|x|<δ ,then $\displaystyle ||(sinx,cosx)-(0,1)||_{max}<\epsilon$ .

    Any suggestions for that delta??
    Try looking at when $\displaystyle \sin(x),1-\cos(x)$ intersect. You obviously want to use $\displaystyle \arcsin(\varepsilon)$. But, what must you impose first?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Jul 2009
    Posts
    107
    I am sorry i do not understand,but if you suggest a delta i can try to prove the problem

    Then you can explain how you got that delta
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Jul 2009
    Posts
    107
    Can anyone help me ,please??
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Jul 2009
    Posts
    107
    perhaps the problem is not derivable??
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove this limit
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 6th 2013, 09:03 AM
  2. Replies: 1
    Last Post: Feb 5th 2010, 03:33 AM
  3. how to prove that any limit ordinal is really a limit?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: Aug 9th 2009, 01:25 AM
  4. Using the Central Limit Theorem to prove a limit
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Mar 23rd 2009, 11:09 AM
  5. Replies: 15
    Last Post: Nov 4th 2007, 07:21 PM

Search Tags


/mathhelpforum @mathhelpforum