lim ((1/(x+4)) = 1/2
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:
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
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.