- #1
tesla93
- 23
- 0
The problem is:
lim as x→- ∞ (-5x/x-2)=-5
And I have to find the best interval of solutions for N
Relevant equations:
if x>N then |(-5x/x-2)-(-5)|<ε
My attempt:
|(-5x/x-2) - (-5)|<ε
|-10/x-2|<ε
x-2< 10/ε
as x→-∞ we can assume that x-2<0
x-2<10/ε
x< (10/ε)+2
therefore, the interval should be NE [(10/ε) +2, -∞)
however, the answer says that it should be -2 not +2. I don't know what I am doing wrong, if anyone can help that would be great! Thanks!
lim as x→- ∞ (-5x/x-2)=-5
And I have to find the best interval of solutions for N
Relevant equations:
if x>N then |(-5x/x-2)-(-5)|<ε
My attempt:
|(-5x/x-2) - (-5)|<ε
|-10/x-2|<ε
x-2< 10/ε
as x→-∞ we can assume that x-2<0
x-2<10/ε
x< (10/ε)+2
therefore, the interval should be NE [(10/ε) +2, -∞)
however, the answer says that it should be -2 not +2. I don't know what I am doing wrong, if anyone can help that would be great! Thanks!