Computing Limits

Factor, cancel, and then substitute.

12 problems · about 22 minutes · TEKS P.1.A

NameDate

Figure — use these to answer the problems

Follow the curve far to the right. It flattens toward zero, which is the limit at infinity.

y = 2/x + 0

Point on the curve4

Figure 1

Straightforward practice. Get the method working first.

5 problems

Limit of (x² − 4) ÷ (x − 2) as x approaches 2?
Answer
2
What does the form 0 ÷ 0 tell you?
- Nothing yet; more algebra is needed.
- The limit is zero.
Limit of (x² − 1) ÷ (x − 1) as x approaches 1?
Answer
Limit of (x² − 36) ÷ (x − 6) as x approaches 6?
Answer
Limit of (6x² + x) ÷ (3x² − 2) as x grows without bound?
Answer

The same ideas with more to keep track of.

3 problems

Limit of (x + 1) ÷ (x² + 3) as x grows without bound?
Answer
Limit of (10x² + 5) ÷ (4x² + 1) as x grows without bound?
Answer
Is 0 ÷ 0 an answer or a signal to do more work? Enter 1 for answer, 2 for signal.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each degree comparison by the limit at infinity it produces.
Write each item under the heading it belongs to: Bottom degree larger · Degrees equal · Degree 1 over degree 3 · Degree 2 over degree 2
Limit is 0
Limit is a ratio of coefficients
Limit of (x² − 49) ÷ (x − 7) as x approaches 7?
Answer
The Cancel
Limit of (x² − 16) ÷ (x − 4) as x approaches 4?
Answer
The Far End
Limit of (4x² + 1) ÷ (2x² + 3) as x grows without bound?
Answer