A general question for limits (1 Viewer)

[mathsbrain]

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

can someone help?

 

[tickboom]

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

 

[Trebla]

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

 

[tickboom]

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?

 

[Trebla]

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).

 

[tickboom]

You can't just square top and bottom.

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

Yes good point well presented!

 

[CM_Tutor]

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 .