Finding limits with absolute values

[Alain12345]

I need help finding limits. I know it's pretty simple most of the time... I know that for example if the lim x--> 3 of x-3, you just plug 3 for x... what do I do if it's the absolute value of x-3?

I know you guys like to see that I've tried to solve the problem, but there's not much I can show you in this case.

Thanks.

 

[courtrigrad]

you have to look at the right and left hand limits (i.e. lim as x approaches a from the left, etc...)

 

[lonelywizard]

If you have an expression that is in indeterminate form, you may try to factor it out. If you cannot factor it, then try multiply it with its conjugate pair.

 

[drpizza]

For absolute value problems, you can write it as a piecewise defined function. i.e. instead of y = abs(x), you can write y = { x, x>=0; -x,x<0

Then, as courtrigard said, look at the left hand and right hand limits.

 

[defansimoh]

Finding d limit of the absolute value of x-3, divided by x-3, for x approuches 0.

lim [x-3]/(x-3)
x->0
Principle [x-3]= {(x-3) if x>4}
{-(x-3) if x<4}

Remember that limit olny exist only if the limit from the negetive side is equal to the limit from the positive side as x approuches the given value!

= lim (x-3)/(x-3) = 1 and =lim -(x-3)/(x-3) = -1
x=>0+ x=>0-
we can conclude by saying
1 is not equal to -1
The limit of [x-3]/x-3 as x=>0 does not exist!