Step by step
The question
Question: find the limit as x → 1 of (x + 3)/(x + 1).
lim x → 1 x + 3x + 1 =
1 Put the number in
Is the bottom 0 at x = 1?
No.
So nothing goes wrong there.
The limit is just the value at 1.
bottom ≠ 0 → just put it in
Put 1 in place of x.
= 1 + 31 + 1
= 42
So the limit is 2.
= 2
2 Check
Let's check with numbers close to 1.
x = 0.99 gives about 2.005.
x = 0.99: f(x) ≈ 2.005
x = 1.01 gives about 1.995.
Both are close to 2.
Right!
x = 1.01: f(x) ≈ 1.995
Let's look back.
First: put the number in.
Last: check.
Answer
= 2