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Cogito

AP Calculus AB · Chapter 1 · Lesson 2

Practice Worksheet

Continuity

Three conditions, all required.

11 problems · about 22 minutes · AP Calculus AB 1.11, 1.13

NameDate

Figure — use these to answer the problems

An infinite discontinuity: the limit fails on both sides.
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y = 1/x + 0
a1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. f(4) = 1 and the limit at 4 is 6. Continuous? 1 for yes, 0 for no.

    Answer

  2. f(3) = 4 and the limit at 3 is 4. Continuous? 1 for yes, 0 for no.

    Answer

  3. f(3) undefined, limit is 4. Continuous? 1 for yes, 0 for no.

    Answer

  4. Sort each discontinuity by whether redefining one point repairs it.

    Write each item under the heading it belongs to: A hole · A jump · A vertical asymptote

    Removable

    Not removable

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Is a polynomial continuous everywhere? 1 for yes, 0 for no.

    Answer

  2. 1/(x − 6). At which x is it discontinuous?

    Answer

  3. A hole at x = 2 with limit 9. What value at 2 would repair it?

    Answer

Stretch Yourself

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

4 problems

  1. Left limit 5, right limit 5, f(1) = 5. Continuous at 1? 1 for yes, 0 for no.

    Answer

  2. How many conditions fail at a vertical asymptote where f is undefined?

    Answer

  3. The Three Conditions

    How many conditions must hold for continuity at a point?

    Answer

  4. The Jump

    Left limit 2, right limit 7. Is this discontinuity removable? 1 for yes, 0 for no.

    Answer