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How do I draw this asymptote graph?

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

y=x4+x2 y = \frac {x}{\sqrt{4 + x^2}}

I have absolutely no idea how to do this.
Reply 1
Original post by JordanL_
As part of a C3 integration question, I need to sketch the graph of

y=x4+x2 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?
Reply 2
Original post by JordanL_
As part of a C3 integration question, I need to sketch the graph of

y=x4+x2 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?
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?
Reply 4
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)
Reply 5
Original post by JordanL_
As part of a C3 integration question, I need to sketch the graph of

y=x4+x2 y = \frac {x}{\sqrt{4 + x^2}}

I have absolutely no idea how to do this.


Differentiate and find turning points.

As x±x \to \pm \infty we have 4+x2x2=xyxxy±1\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.
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?
Reply 7
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
Okay, thanks both for the help!

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