Step by step
The question
Question: find the limit as x → −2 of (x² − 3x).
lim x → −2 (x2 − 3x) =
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.
= (−2)2 − 3(−2)
Careful!
We put in (−2), in brackets.
−2 squared is plus 4.
Careful: not −2² = −4 ✗
= 4 + 6
So the limit is 10.
= 10
2 Check
Let's check with numbers close to −2.
x = −2.01 gives about 10.0701.
x = −2.01: f(x) ≈ 10.0701
x = −1.99 gives about 9.9301.
Both are close to 10.
Right!
x = −1.99: f(x) ≈ 9.9301
Let's look back.
First: put the number in.
Last: check.
Answer
= 10