lim ((1/(x+4)) = 1/2
x-> -2
or
a=-2
L=1/2
f(x)= (1/(x+4))
The question says we will need a constraint on |x+2|, so it says to assume |x+2|<1.
This is the part that is confusing me because I can solve any other limit question.
The options for answers are:
a)[0,min{1,4epsilon})
b)(0,min{1,6epsilon}]
c)[0,min{1,2epsilon})
d)(0,min{1,2epsilon}]
e)(0,min{1,4epsilon})
So would the answer be D???
Because if you plug 1 as the |x+4|, from the equation you gave me: 1|x+2|/2|x+4|<epsilon
I would get |x+2|<2*epsilon
I don't really know if i've done that correctly, I've been doing work all day and my head is swimming with different subjects
To show you need to prove . So you need to show .
Scratch work:
But we can't let because is only supposed to be a function of , not a function of . But if we remember that the act of taking a limit means that we are showing that moving closer to the value of in both directions moves closer to the value of in both directions, that means we can choose a value of as close to as we like, then make it move closer. So say we want to start off with no more than unit away from , then . Therefore
So we can let and reverse each step to get your proof.