Step by step
The question
Question: find the limit as x → 1 of (x² + 4).
lim x → 1 (x2 + 4) =
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 = 1.
no gaps, no jumps → just put it in
Put 1 in place of x.
= 12 + 4
= 1 + 4
So the limit is 5.
= 5
2 Check
Let's check with numbers close to 1.
x = 0.99 gives about 4.9801.
x = 0.99: f(x) ≈ 4.9801
x = 1.01 gives about 5.0201.
Both are close to 5.
Right!
x = 1.01: f(x) ≈ 5.0201
Let's look back.
First: put the number in.
Last: check.
Answer
= 5