Where does the 5 come from in the red underlined?
#Meaning of x+2<5 in this ε-δ problem?
teal venture
spare hatchBOT
surreal geyser
Where does the 5 come from in the red underlined?
The author has simply noted that:
$\$ if $x \ \in \ (1, 3)$, i.e. $1 \ < \ x \ < \ 3: \ 1 + 2 \ < \ x + 2 \ < \ 3 + 2 $ (Added 2 everywhere) $\$ Thus $x+2 \ < \ 5$
devout oasisBOT
UnexpectedTaco
teal venture
**UnexpectedTaco**
Why is only 5 shown though?
surreal geyser
Why is only 5 shown though?
As in? You wish to achieve x+2 and 5 is the upper bound for it.
teal venture
As in? You wish to achieve x+2 and 5 is the upper bound for it.
Why is the upper bound, 5, important?
limber epoch
Why is the upper bound, 5, important?
You need to make sure |x+2| doesn’t get arbitrarily large. Using 5 in particular isn’t special, you just need any upper bound of |x+2| when x takes values between (1,3)
fresh cloud
Where does the 5 come from in the red underlined?
They're making an initial delta interval of radius 1 around your x=2. Not sure if that makes sense @teal venture
teal venture
They're making an initial delta interval of radius 1 around your x=2. Not sure i...
What does that mean?
fresh cloud
What does that mean?
Do you see how the interval $(1,3)$ is perfectly centered at $2$? You could write it as $(2-1, 2+1)$, yeah?
devout oasisBOT
SWR
