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Cogito

AP Calculus BC · Chapter 5 · Lesson 1

Practice Worksheet

Taylor and Maclaurin Series

A function rebuilt from its derivatives at one point.

11 problems · about 26 minutes · AP Calculus BC 10.11, 10.13, 10.14

NameDate

Figure — use these to answer the problems

The exponential is the function whose series is easiest to remember.
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y = 1 · 2^x + 0
a1
b2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. What is 6! ?

    Answer

  2. What is 3! ?

    Answer

  3. What is 5! ?

    Answer

  4. In the series for eˣ, what is the coefficient of x²? Give the denominator.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. The series for sin x has only which powers? 1 for odd, 2 for even.

    Answer

  2. The series for cos x has only which powers? 1 for odd, 2 for even.

    Answer

  3. A Taylor series centred at 3 is called a Maclaurin series. 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

4 problems

  1. Evaluate 1 + x + x²/2 at x = 0.

    Answer

  2. Select every true statement about Taylor series.

    • It matches the derivatives at the centre.
    • It equals the function everywhere.
    • It is only valid inside its interval of convergence.
    • It must be centred at zero.
    • Tick every box that applies.

  3. The Factorial

    What is 4! ?

    Answer

  4. The Centre

    A Maclaurin series is centred at which value?

    Answer