Finding limits when there is an absolute value in the numerator

[katielynn09]

Ok the problem is:
lim x->-1 |x+1| / x²-1
(sorry i don't really know how to type the equation out)

I think that you have to find the limit as x->-1 from both the left and right sides

from right:
so I got lim x->-1 = (x+1)/x²-1 = (x+1)/(x+1)(x-1) = 1/(x-1) =1/-1-1 =-1/2


How would I go about finding the limit from the left?

 

[tiny-tim]

Welcome to PF!

Ok the problem is:
lim x->-1 |x+1| / x²-1
(sorry i don't really know how to type the equation out)

I think that you have to find the limit as x->-1 from both the left and right sides

from right:
so I got lim x->-1 = (x+1)/x²-1 = (x+1)/(x+1)(x-1) = 1/(x-1) =1/-1-1 =-1/2


How would I go about finding the limit from the left?

Hi katielynn09! Welcome to PF!

Just start: "from the left, |x + 1| / x²-1 = -(x + 1) / x²-1 … "

 

[katielynn09]

Hi katielynn09! Welcome to PF!

Thanks!

Just start: "from the left, |x + 1| / x2-1 = -(x + 1) / x2-1 … "

Ok I understand that now. I'm flipped around though. I can't use factoring like I did before because it won't cancel out or substitution because the denominator would still equal 0. What technique would I use to find the limit now?

can i sort of ignore the negative sign like -1(x+1)/(x+1)(x-1) = -1/-1-1 = 1/2 ?

 

[tiny-tim]

Ok I understand that now. I'm flipped around though. I can't use factoring like I did before …

Hi katielynn09!

ooh, you are flipped aren't you?

yes you can use factoring … the top is just another factor (which happens to be -1) times before …

ignore the -1, then factor, then put the -1 back again!

 

[katielynn09]

thank you :)