A general question for limits (1 Viewer)

mathsbrain

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Was just trying out a few things with first principles and got stuck at one point:

can someone help?
 

tickboom

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Is it 1? ... My instinct was to try and get that x out of the denominator ...

Pic.jpg
 

Trebla

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The limit is undefined (unless x is coming from a specified direction) because the square root of x^2 is |x|, not x
 

tickboom

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The limit is undefined (unless x is coming from a specified direction) because the square root of x^2 is |x|, not x
Oooooh yes very good point! ... What about this approach? (I squared top and bottom to simplify instead) ... Or does this approach also have an issue?

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Trebla

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I don’t quite follow what you did there, but the answer is definitely not 1. You can plot a graph and see for yourself that the limit is undefined (at least for the two-sided limit).
 

blyatman

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You can't just square top and bottom.

It would be like saying:
x = 1
So x^2 = 1
So x = +-1.
 

CM_Tutor

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I can similarly rewrite


and so get the limit as -1 after cancelling and substituting .

As Trebla notes,


giving the limit as 1 from above and -1 from below, making the limit undefined and the curve discontinuous at .
 

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