Step by step
The question
Question: find the limit as x → 2 of (3x − 5).
lim x → 2 (3x − 5) =
1 Put the number in
This is a polynomial.
Its graph has no gaps and no jumps.
So the limit is just its value at x = 2.
no gaps, no jumps → just put it in
Put 2 in place of x.
= 3(2) − 5
= 6 − 5
So the limit is 1.
= 1
2 Check
Let's check with numbers close to 2.
x = 1.99 gives about 0.97.
x = 1.99: f(x) ≈ 0.97
x = 2.01 gives about 1.03.
Both are close to 1.
Right!
x = 2.01: f(x) ≈ 1.03
Let's look back.
First: put the number in.
Last: check.
Answer
= 1