Results 1 to 7 of 7

Math Help - evaluate limits

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    37

    evaluate limits

    Hi all! Here is my question which I am stuck on:
    (its actually in 2 parts)
    (a) If \rightarrow\mathbb{R}" alt="f\rightarrow\mathbb{R}" />, with D= { x | x is irrational} and f(x) =\frac{2x}{x-3}, evaluate \lim_{x\to\infty}f(x) and prove the result.

    (b) If f:\mathbb{Q}\rightarrow\mathbb{R} is defined by f(x)=\frac{x^2+1}{x-2}, evaluate \lim_{x\to-\infty}f(x) and prove the result.

    What do I do?
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by binkypoo View Post
    Hi all! Here is my question which I am stuck on:
    (its actually in 2 parts)
    (a) If \rightarrow\mathbb{R}" alt="f\rightarrow\mathbb{R}" />, with D= { x | x is irrational} and f(x) =\frac{2x}{x-3}, evaluate \lim_{x\to\infty}f(x) and prove the result.

    (b) If f:\mathbb{Q}\rightarrow\mathbb{R} is defined by f(x)=\frac{x^2+1}{x-2}, evaluate \lim_{x\to-\infty}f(x) and prove the result.

    What do I do?
    Thanks
    Algabraic manipulation is your friend.

    Here's something to get you started on the first one:

     \frac{2x}{x - 3} = \frac{x(2)}{x(1 - \frac{3}{x})}  = \frac{2}{1 - \frac{3}{x}}
    Last edited by Mush; October 17th 2009 at 07:58 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    37
    I see that but I dont know where to go from there, ie using the definition of limits to infinity to prove it !
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576
    Quote Originally Posted by binkypoo View Post
    I see that but I dont know where to go from there, ie using the definition of limits to infinity to prove it !
    What happens to \frac{3}{x} as x \to \infty?

    Using this, what happens to

    \frac{2}{1 - \frac{3}{x}} as x \to \infty?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576
    Quote Originally Posted by binkypoo View Post
    Hi all! Here is my question which I am stuck on:
    (its actually in 2 parts)
    (a) If \rightarrow\mathbb{R}" alt="f\rightarrow\mathbb{R}" />, with D= { x | x is irrational} and f(x) =\frac{2x}{x-3}, evaluate \lim_{x\to\infty}f(x) and prove the result.

    (b) If f:\mathbb{Q}\rightarrow\mathbb{R} is defined by f(x)=\frac{x^2+1}{x-2}, evaluate \lim_{x\to-\infty}f(x) and prove the result.

    What do I do?
    Thanks
    b)
    \frac{x^2 + 1}{x - 2} = \frac{x^2 - 4 + 5}{x - 2}

     = \frac{x^2 - 4}{x - 2} + \frac{5}{x - 2}

     = \frac{(x + 2)(x - 2)}{x - 2} + \frac{5}{x - 2}

     = x + 2 + \frac{5}{x - 2}.

    Now take the limit as x \to -\infty.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Oct 2009
    Posts
    37
    so because \lim_{x\to -\infty}x = -\infty, it doesnt really matter what the limit of the other two terms are, it will still be -\infty right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Well, it would matter if the limit of the other terms went to +\infty (then you would have to be more careful), but since it obviously doesn't, no, it doesn't matter.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. hwo to evaluate these limits?!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 14th 2010, 05:35 PM
  2. Evaluate limits
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 21st 2010, 03:43 PM
  3. Evaluate Limits
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 19th 2010, 08:00 PM
  4. Evaluate limits:
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 22nd 2009, 02:42 PM
  5. Evaluate some limits
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 3rd 2008, 01:30 PM

Search Tags


/mathhelpforum @mathhelpforum