- #1
NickBE
- 2
- 0
Hello, I am trying to prove the following...
lim (x+3) [tex]\left|x+5\right|[/tex][tex]/x+5[/tex]
x[tex]\rightarrow-5[/tex]
from the left, L=+2
from the right, L=-2
I used delta-epsilon on the right hand limit and got [tex]\delta[/tex] = [tex]\epsilon[/tex]
However, I'm not sure how to proceed when I get to this step while trying to prove the left hand limit:
[tex]\left|x+1\right|[/tex]< [tex]\epsilon[/tex] if 0<[tex]\left|x+5\right|[/tex]<[tex]\delta[/tex]
lim (x+3) [tex]\left|x+5\right|[/tex][tex]/x+5[/tex]
x[tex]\rightarrow-5[/tex]
from the left, L=+2
from the right, L=-2
I used delta-epsilon on the right hand limit and got [tex]\delta[/tex] = [tex]\epsilon[/tex]
However, I'm not sure how to proceed when I get to this step while trying to prove the left hand limit:
[tex]\left|x+1\right|[/tex]< [tex]\epsilon[/tex] if 0<[tex]\left|x+5\right|[/tex]<[tex]\delta[/tex]