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Cogito

Precalculus · Chapter 8 · Lesson 1

Practice Worksheet

The Idea of a Limit

Where a function is heading, not where it lands.

12 problems · about 21 minutes · TEKS P.1.A

NameDate

Figure — use these to answer the problems

Slide the point toward zero from either side. The values run away, which is a limit that does not exist.
-8-8-6-6-4-4-2-222446688
y = 1/x + 0
  • Point(2, 0.50)
a1
Point on the curve2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Limit of 4x − 2 as x approaches 3?

    Answer

  2. A function is undefined at x = 2. Can its limit at 2 exist?

    • Yes, a limit describes approach, not arrival.
    • No, the function must be defined there.

  3. Limit of 3x as x approaches 4?

    Answer

  4. Limit of x² as x approaches 5?

    Answer

  5. Limit of (x² − 9) ÷ (x − 3) as x approaches 3?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Limit of 7 as x approaches 2?

    Answer

  2. Left limit is 3 and right limit is 5. Does the two-sided limit exist? 1 for yes, 0 for no.

    Answer

  3. Limit of (x² − 25) ÷ (x − 5) as x approaches 5?

    Answer

Stretch Yourself

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

4 problems

  1. Which situations mean a limit does not exist?

    • The two sides approach different values
    • The values run off to infinity
    • There is a hole in the graph
    • The function value differs from the limit
    • Tick every box that applies.

  2. Limit of x + 8 as x approaches −3?

    Answer

  3. The Approach

    What is the limit of 2x + 1 as x approaches 3?

    Answer

  4. The Hole

    What is the limit of (x² − 4) ÷ (x − 2) as x approaches 2?

    Answer