Results 1 to 4 of 4

Math Help - Limits from first principles, L'Hopital's Rule - urgent help

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    3

    Exclamation Limits from first principles, L'Hopital's Rule - urgent help

    Hi I would like to know if anyone can help me or guide me through the steps to the answers to these questions? I am fairy new to advanced mathematics and I am finding it a bit difficult to understand some topics...sigh... ur help would be greatly appreciated

    1. Determine the limit from first prinicples by evaluating the function at values about the indicated limiting value.

    lim [(x^3) - x]/(x-1)
    x-->1


    2. Evaluate;

    lim [2- √(x+2)] / (x-2)
    x-->2


    3. A 5-Ω resistor and a variable resistor of resistance R are placed in parallel. The expression for the resulting resistance, Rτ, is given by
    Rτ= 5R/ (5 +R). Determine the limiting value of Rτ as R-->.(Use L'Hopital's Rule)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2009
    Posts
    290
    1) Factor the numerator.

    2) Rationalize the numerator

    3) Divide numerator and denominator by the highest power variable (in this case x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,004
    Thanks
    1660
    Quote Originally Posted by Mythichaos View Post
    Hi I would like to know if anyone can help me or guide me through the steps to the answers to these questions? I am fairy new to advanced mathematics and I am finding it a bit difficult to understand some topics...sigh... ur help would be greatly appreciated

    1. Determine the limit from first prinicples by evaluating the function at values about the indicated limiting value.

    lim [(x^3) - x]/(x-1)
    x-->1
    The phrasing "by evaluating the function at values about the indicated limiting value" implies that you are expected to calculate \frac{x^3- 1}{x-1} for things like x= 0.9, 0.99, 0.999, 1.001, 1.01, 1.1 and then "guess" the limit. Of course, calculating any finite number of points won't actually tell you the limit for certain.


    2. Evaluate;

    lim [2- √(x+2)] / (x-2)
    x-->2
    Multiply both numerator and denominator by 2+ \sqrt{x+2} (rationalize the numerator).


    3. A 5-Ω resistor and a variable resistor of resistance R are placed in parallel. The expression for the resulting resistance, Rτ, is given by
    Rτ= 5R/ (5 +R). Determine the limiting value of Rτ as R-->.(Use L'Hopital's Rule)
    What is the derivative of 5R with respect to R? What is the derivative of 5+ R with respect to R? Do you know what "L'Hopital's Rule" is?
    Here, I agree with Chengben that L'Hopital's rule is not the simplest way to do this. (But the variable is "R", not "x"!)
    Last edited by Chris L T521; September 23rd 2009 at 07:16 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2009
    Posts
    3
    ok.... for the second one.....
    the answer :

    lim [2- √(x+2)] / (x-2) = lim [2- √(x+2)] [2+ √(x+2)]/ (x-2) [2+ √(x+2)]
    x-->2 x-->2

    = lim [4 + 2√(x+2) - 2√(x+2) - (x+2)] / (x-2) [2+ √(x+2)]
    x-->2

    = lim (4 - x + 2) / (x-2) [2+ √(x+2)]
    x-->2

    .......then.... ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Limits using L'Hopital's Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 11th 2011, 01:53 PM
  2. find limits using L'Hopital rule and FTC
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 13th 2011, 05:05 PM
  3. Replies: 1
    Last Post: April 24th 2010, 01:40 PM
  4. Using L'Hopital's Rule To Evaluate Limits
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 8th 2010, 02:37 AM
  5. limits(l'hopital's rule)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 16th 2008, 05:42 AM

Search Tags


/mathhelpforum @mathhelpforum