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Cogito

Calculus · Chapter 1 · Lesson 1

Practice Worksheet

What a Limit Is

Where a function is heading, not where it arrives.

8 problems · about 21 minutes · LIM-1.A, LIM-1.C

NameDate

Figure — use these to answer the problems

Move the point towards zero from each side and watch where the curve heads.
-8-8-6-6-4-4-2-222446688
y = 1/x + 0
  • Point(2, 0.50)
Numerator1
Shift up by0
x approaches2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Limit of (x² − 36)/(x − 6) as x approaches 6?

    Answer

  2. What does a limit describe?

    • Where the function is heading as x approaches the point.
    • The value of the function at the point.

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

    Answer

  4. Limit of (x² − 9)/(x − 3) as x approaches 3?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Limit of (x² − 25)/(x − 5) as x approaches 5?

    Answer

  2. Must a function be defined at a point to have a limit there?

    • No.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Limit

    The limit of (x² − 4)/(x − 2) as x approaches 2. What is it?

    Answer

  2. The Direct One

    The limit of 3x + 1 as x approaches 5. What is it?

    Answer