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Given the limit of a function, deduce the value of some variables inside the function

  1. Aug 11, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm doing an assignment, and I've hit a wall with this limits question:

    6. If the limit as x approaches 0 of [URL]http://www2.wolframalpha.com/Calculate/MSP/MSP202919ggbg4de783c0e7000024ba5hah2cdg59e6?MSPStoreType=image/gif&s=14&w=106&h=41[/URL] equals [itex]\sqrt{5}[/itex], deduce the values of a and b.


    3. The attempt at a solution

    So far, I've multiplied the numerator and denominator by the conjugate, and now I have [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP231719ggb7fd1fig87b800001ie7f55ge9hc9190?MSPStoreType=image/gif&s=9&w=106&h=42. [Broken] I've tried squaring the bottom and the top and expanding them out, but I'm just spinning my wheels at this point, I don't really know how to proceed. I would appreciate any hints you could give me, thanks in advance.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 11, 2011 #2

    eumyang

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    Re: Given the limit of a function, deduce the value of some variables inside the func

    Are the fractions in the images correct? Because if I multiply
    [itex](\sqrt{a+bx}-\sqrt{5})(\sqrt{a+bx}+\sqrt{5})[/itex]
    I get
    a + bx - 5,
    and that's not what's in the numerator of the 2nd image.
     
    Last edited by a moderator: May 5, 2017
  4. Aug 11, 2011 #3
    Re: Given the limit of a function, deduce the value of some variables inside the func

    Sorry, I left out this part -[PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP157319ggbcc94ih84dd300005ia505e2i20325d5?MSPStoreType=image/gif&s=24&w=126&h=46 [Broken] - that's what I got after multiplying by the conjugate, then I tried to cancel the x to get rid of the division by zero at the limit
     
    Last edited by a moderator: May 5, 2017
  5. Aug 11, 2011 #4
    Re: Given the limit of a function, deduce the value of some variables inside the func

     
    Last edited by a moderator: May 5, 2017
  6. Aug 11, 2011 #5

    eumyang

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    Homework Helper

    Re: Given the limit of a function, deduce the value of some variables inside the func

    You mean that you tried to cancel the x going from this:
    [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP157319ggbcc94ih84dd300005ia505e2i20325d5?MSPStoreType=image/gif&s=24&w=126&h=46 [Broken]
    to this?
    [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP231719ggb7fd1fig87b800001ie7f55ge9hc9190?MSPStoreType=image/gif&s=9&w=106&h=42 [Broken]
    If so, then you can't do that.
     
    Last edited by a moderator: May 5, 2017
  7. Aug 11, 2011 #6
    Re: Given the limit of a function, deduce the value of some variables inside the func

    I did this step, I should have included it in the OP. anyway yes I am from Auckland University, I am terrible at maths but decided to do 108 anyway, which is starting to look like it may have been a mistake:rofl:
     
  8. Aug 11, 2011 #7
    Re: Given the limit of a function, deduce the value of some variables inside the func

    Thanks eumyang, I'll try again.
     
  9. Aug 11, 2011 #8
    Re: Given the limit of a function, deduce the value of some variables inside the func

    Hint (copied directly from your assignment): Multiply the numerator and denominator by the conjugate and remember that the denominator can not be zero.

    The bolded part means that a=5.
     
  10. Aug 11, 2011 #9
    Re: Given the limit of a function, deduce the value of some variables inside the func

    Thanks Harrisonized, didn't realise the hint about the denominator meant a=5
     
  11. Aug 15, 2011 #10
    Re: Given the limit of a function, deduce the value of some variables inside the func

    So how do we deduce that a=5 from that? I am at this step: (a+bx-5)/(x√(a+bx)+√5))
    but unsure how to move forward from there.
     
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