Page 1 of 2 12 LastLast
Results 1 to 15 of 25

Math Help - Indeterminate Forms

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Indeterminate Forms

    Hi guys, I'm working through a bunch of problems in which I have to determine the type of indeterminate form (i.e. infin/infin, 0/0). This one is throwing me for a loop though:

    $\underset{x\to -{3}^{-}}{lim}\left(\frac{x}{{x}^{2}+2x-3}-\frac{4}{x+3}\right)$

    When I substitute in the -3, I get 3/0 - 4/0, but I obviously can't divide by 0. What is the indeterminate form in this case?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Indeterminate Forms

    Quote Originally Posted by kwikness View Post
    Hi guys, I'm working through a bunch of problems in which I have to determine the type of indeterminate form (i.e. infin/infin, 0/0). This one is throwing me for a loop though:

    $\underset{x\to -{3}^{-}}{lim}\left(\frac{x}{{x}^{2}+2x-3}-\frac{4}{x+3}\right)$

    When I substitute in the -3, I get 3/0 - 4/0, but I obviously can't divide by 0. What is the indeterminate form in this case?
    Start by expressing it all over a common denominator and then simplify. Note that x^2 + 2x - 3 = (x+3)(x-1) ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Re: Indeterminate Forms

    Thanks for the reply.

    I've tried simplifying it down to:

    \frac{3x-4}{(x-1)(x+3)}

    But still, when I plug in -3, I get -13/0.
    Last edited by mr fantastic; July 27th 2011 at 07:41 PM. Reason: Fixed latex.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Indeterminate Forms

    Quote Originally Posted by kwikness View Post
    Thanks for the reply.

    I've tried simplifying it down to:
    $\frac{3x-4}{\left(I-x\right)\left(x+3\right)}$

    But still, when I plug in -3, I get -13/0.
    Yes, so what does that tell you ....? What would a graph of the function look like? (NOte that the form is no longer indeterminant ....)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29

    Re: Indeterminate Forms

    Quote Originally Posted by kwikness View Post
    Hi guys, I'm working through a bunch of problems in which I have to determine the type of indeterminate form (i.e. infin/infin, 0/0). This one is throwing me for a loop though:

    $\underset{x\to -{3}^{-}}{lim}\left(\frac{x}{{x}^{2}+2x-3}-\frac{4}{x+3}\right)$

    When I substitute in the -3, I get 3/0 - 4/0, but I obviously can't divide by 0. What is the indeterminate form in this case?
    Maybe this will help,

    \displaystyle \lim_{x\to -3}\left(\frac{x}{{x}^{2}+2x-3}\times \frac{\frac{1}{x^2}}{\frac{1}{x^2}}-\frac{4}{x+3}\times \frac{\frac{1}{x}}{\frac{1}{x}}\right)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Re: Indeterminate Forms

    It looks like there's a vertical asymptote in the graph, but the graph runs through the x axis at (-3,0)

    Does that mean the correct answer is that this is NOT an indeterminate form?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Re: Indeterminate Forms

    pickslides, your avatar is the balls, but I can't make sense of how your hint helps as those additions are really just 1s and I'm left with the same equation when I plug in the -3.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Indeterminate Forms

    Quote Originally Posted by kwikness View Post
    It looks like there's a vertical asymptote in the graph, but the graph runs through the x axis at (-3,0)

    Does that mean the correct answer is that this is NOT an indeterminate form?
    -13/0 => the limit will be either +oo or -oo. You need to figure out which.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Indeterminate Forms

    Quote Originally Posted by kwikness View Post
    Hi guys, I'm working through a bunch of problems in which I have to determine the type of indeterminate form (i.e. infin/infin, 0/0). This one is throwing me for a loop though:

    $\underset{x\to -{3}^{-}}{lim}\left(\frac{x}{{x}^{2}+2x-3}-\frac{4}{x+3}\right)$

    When I substitute in the -3, I get 3/0 - 4/0, but I obviously can't divide by 0. What is the indeterminate form in this case?
    What are all of the indeterminate forms you have learned?

    How does \lim_{x\to-3^-} differ from \lim_{x\to-3^+}\,?

    It may help to factor x^2+2x-3\,, but I think it's a mistake to combine the fractions into one fraction.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Indeterminate Forms

    Quote Originally Posted by SammyS View Post
    [snip]

    It may help to factor x^2+2x-3\,, but I think it's a mistake to combine the fractions into one fraction.
    I don't see why it would be a mistake. Doing so makes it very clear that it will be one of -oo or +oo.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Indeterminate Forms

    Quote Originally Posted by mr fantastic View Post
    I don't see why it would be a mistake. Doing so makes it very clear that it will be one of -oo or +oo.
    Yes, this will give the desired limit, but the assignment was to determine the indeterminate form of the original expression.

    Some possible indeterminate forms: 0/0, ∞/∞, 0∞, ∞ - ∞, -∞ + ∞, 1^∞, ∞^0, 0^0 etc
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Indeterminate Forms

    Quote Originally Posted by SammyS View Post
    Yes, this will give the desired limit, but the assignment was to determine the indeterminate form of the original expression.

    Some possible indeterminate forms: 0/0, ∞/∞, 0∞, ∞ - ∞, -∞ + ∞, 1^∞, ∞^0, 0^0 etc
    Well, it is one of the forms in your list. And post #1 (of all posts, the original question) suggests what the answer is ....
    Last edited by mr fantastic; July 28th 2011 at 02:41 PM.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Indeterminate Forms

    Yes.

    However, it appears that kwikness (OP) does get what happens as the denominator approaches zero.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Re: Indeterminate Forms

    Quote Originally Posted by SammyS View Post
    Yes.

    However, it appears that kwikness (OP) does get what happens as the denominator approaches zero.
    Right. Applying L'Hopital's rule will yield an answer of infinity. What I don't understand is which of the indeterminate forms the original equation comes out to because of the zeroes in the denominator.
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Indeterminate Forms

    Do the denominators approach 0 from the right (the positive side of zero) or from the left (the negative side) as x approaches -3 from the left?
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Indeterminate Forms
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 16th 2010, 05:50 AM
  2. Indeterminate Forms
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 8th 2010, 04:31 PM
  3. Indeterminate forms help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2010, 01:30 PM
  4. indeterminate forms
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 18th 2009, 09:24 PM
  5. please help with limits of indeterminate forms
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 19th 2009, 08:18 PM

Search Tags


/mathhelpforum @mathhelpforum