Step by step
The question
Question: find the limit as x → 3 of (x² + 2x − 1).
lim x → 3 (x2 + 2x − 1) =
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 = 3.
no gaps, no jumps → just put it in
Put 3 in place of x.
= 32 + 2(3) − 1
= 9 + 6 − 1
So the limit is 14.
= 14
2 Check
Let's check with numbers close to 3.
x = 2.99 gives about 13.9201.
x = 2.99: f(x) ≈ 13.9201
x = 3.01 gives about 14.0801.
Both are close to 14.
Right!
x = 3.01: f(x) ≈ 14.0801
Let's look back.
First: put the number in.
Last: check.
Answer
= 14