Step by step
The question
Question: find the limit as x → 4 of (x − 2)/(x + 2).
lim x → 4 x − 2x + 2 =
1 Put the number in
Is the bottom 0 at x = 4?
No.
So nothing goes wrong there.
The limit is just the value at 4.
bottom ≠ 0 → just put it in
Put 4 in place of x.
= 4 − 24 + 2
= 26
So the limit is 1/3.
= 13
2 Check
Let's check with numbers close to 4.
x = 3.99 gives about 0.3322.
x = 3.99: f(x) ≈ 0.3322
x = 4.01 gives about 0.3344.
Both are close to 1/3.
Right!
x = 4.01: f(x) ≈ 0.3344
Let's look back.
First: put the number in.
Last: check.
Answer
= 13