Results 1 to 7 of 7

Math Help - limit in calculus

  1. #1
    Newbie
    Joined
    Oct 2006
    Posts
    17

    limit in calculus

    I'm taking a calculus course in first year of university. There's a limit in my text I cannot seem to solve. Here it is, lim x to 0 of [(x+1)^(1/3) - 1]/x. The answers at the back say the limit is 1/3, but how would you re-arrange it to get this? NOTE: I cannot use L'Hopital's Rule. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,658
    Thanks
    1615
    Awards
    1
    Quote Originally Posted by BenWong View Post
    I'm taking a calculus course in first year of university. There's a limit in my text I cannot seem to solve. Here it is, lim x to 0 of [(x+1)^(1/3) - 1]/x. The answers at the back say the limit is 1/3, but how would you re-arrange it to get this? NOTE: I cannot use L'Hopital's Rule. Thanks.
    Multiply this out.
    \frac{{\sqrt[3]{{x + 1}} - 1}}{x}\left( {\frac{{\sqrt[3]{{\left( {x + 1} \right)^2 }} + \sqrt[3]{{x + 1}} + 1}}{{\sqrt[3]{{\left( {x + 1} \right)^2 }} + \sqrt[3]{{x + 1}} + 1}}} \right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    More easy:

    Substitute u^3=x+1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2006
    Posts
    17
    This one is similar. lim x to 0 of (sqrt(1+x) - sqrt(1-x))/x. I rationalized it to get 2/[sqrt(1+x) - sqrt(1-x)], but this doesn't make it any better. What do I do now?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by BenWong View Post
    This one is similar. lim x to 0 of (sqrt(1+x) - sqrt(1-x))/x. I rationalized it to get 2/[sqrt(1+x) \color{red}+ sqrt(1-x)], that should've been positive.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2006
    Posts
    17
    Yeah, that last one was a dumb mistake. Last one I don't know.
    lim x to 1 of (x^2 - 3x + 2)/(x^3 - 3x^2 + 2).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    All you need to do, it's to factorise top & bottom, 'cause there's a factor which produces the indetermination.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculus Limit Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 10th 2010, 11:16 PM
  2. Replies: 11
    Last Post: September 7th 2009, 04:57 PM
  3. Calculus Limit Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 12th 2009, 01:42 PM
  4. Calculus Limit Problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 8th 2008, 10:45 PM
  5. Limit for multivariable calculus
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 16th 2008, 06:22 PM

Search Tags


/mathhelpforum @mathhelpforum