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    As part of a C3 integration question, I need to sketch the graph of

     y = \frac {x}{\sqrt{4 + x^2}}

    I have absolutely no idea how to do this.
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    (Original post by JordanL_)
    As part of a C3 integration question, I need to sketch the graph of

     y = \frac {x}{\sqrt{4 + x^2}}

    I have absolutely no idea how to do this.
    Could you link us to the full question or take a picture of it? Does the question have a pre-existing diagram or explanation?
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    (Original post by JordanL_)
    As part of a C3 integration question, I need to sketch the graph of

     y = \frac {x}{\sqrt{4 + x^2}}

    I have absolutely no idea how to do this.
    bit hard but what happens as x gets very large and positive?
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    (Original post by Zacken)
    Could you link us to the full question or take a picture of it? Does the question have a pre-existing diagram or explanation?
    Here it is, no diagram or anything (q8):


    (Original post by TeeEm)
    bit hard but what happens as x gets very large and positive?
    I guess y increases and the gradient decreases?
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    (Original post by JordanL_)

    ....
    I suggest check what y does.
    you take a calculator and substitute larger and large values of x (positive)
    then repat with smaller and smaller values of x (smaller = negative and larger)
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    (Original post by JordanL_)
    As part of a C3 integration question, I need to sketch the graph of

     y = \frac {x}{\sqrt{4 + x^2}}

    I have absolutely no idea how to do this.
    Differentiate and find turning points.

    As x \to \pm \infty we have \sqrt{4+x^2} \approx \sqrt{x^2} = |x| \Rightarrow y \approx \frac{x}{|x|} \Rightarrow y \to \pm 1.

    I will leave you in TeeEm's hands now as I am going to bed.
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    (Original post by TeeEm)
    I suggest check what y does.
    you take a calculator and substitute larger and large values of x (positive)
    then repat with smaller and smaller values of x (smaller = negative and larger)
    Okay, thanks - so I see that as x tends to infinity/negative infinity, y will tend to +- 1. I assumed that I was meant to know how to sketch it just from the equation, but I guess not.

    Is that the method you'd use in an exam - just substitute values of x to find the asymptotes? Or do it the way Zacken did it?
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    (Original post by JordanL_)
    Okay, thanks - so I see that as x tends to infinity/negative infinity, y will tend to +- 1. I assumed that I was meant to know how to sketch it just from the equation, but I guess not.

    Is that the method you'd use in an exam - just substitute values of x to find the asymptotes? Or do it the way Zacken did it?
    both methods work...
    whatever works for you
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    Okay, thanks both for the help!
 
 
 
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