Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

One Sided Limits Help?

Okay, I feel that I have a pretty good idea what I'm doing, for the most part. I can't figure this one out at all, though.

http://awesomescreenshot.com/01d194ih23

I know I need to manipulate the equation somehow, but I have no idea how.

Thanks.

1 Answer

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  • 7 years ago
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    So...

    You want to look to get rid of that nasty divide by (y-1).

    So you want to have (y-1)(?) in your numerator so you can eliminate the y-1 and change it from a division to a straight quadratic ideally.

    i.e (y-1)(?)/(y-1)

    Now it is reasonably obvious that just taking y-1 outside of y^3-1 doesn't lead to a nice function in the form (y-1)(A+/-B)

    Nevertheless its worth trying to take it outside and we can hope the remainder will have a y-1 factor in it also!

    so...

    (y-1)(A+/-B)

    We want to pick A and B to try and get the result as close as possible to y^3-1

    Lets try A=y^2 to give us the desired y^3 element (from y*y^2) and B as +1 to give us the desired -1 (from -1*+1)

    So we have:

    (y-1)(y^2+1) = y^3+y-y^2-1 =(y^3-1)+y-y^2

    Note this has the desired y^3-1 but also has an undesired y-y^2

    So we will need to get rid of this by adding its negative on the end:

    (y-1)(y^2+1)-y+y^2

    Now what to do with the -y+y^2... Have a think about factoring this to get (y-1) in this part also....

    I haven't answered it but have started you in the direction!

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