This question was posed by a student.

**Explanation**

Exact versus approximation. The two curves depart from each other at x=pi/5

When we use the approximation to compute the volume, it differs significantly from the exact volume.

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# Category: Maclaurin’s series

## Approximation in series expansion

## Challenging Maclaurin’s series problem 2

## Challenging Maclaurin’s series problem 1

## Quick Maclaurin’s series expansion using GC

This question was posed by a student.

**Explanation**

Exact versus approximation. The two curves depart from each other at x=pi/5

When we use the approximation to compute the volume, it differs significantly from the exact volume.

(i) find the Maclaurin’s series of f(x) up to and including the term in .

(ii) Hence deduce the series expansion of the function up to and including the term in

**Solution**

(i) is routine, can easily work out to be

(ii) requires Higher Order Thinking (HOT)

We differentiate the series obtained in (i) to get

Principle used: Differentiate one series expansion to get the series expansion for another series.

In Maclaurin’s series expansion, where up to f”(0) need to be evaluated, can be done quickly using the GC.

**Example**

Using TI 84 Plus (OS 2.55)

From G.C,

f(0)= 3/2

f'(0) = -3/4

f”(0)= 5/4

Therefore using Maclaurin’s series expansion,

If powers higher than 2 such as 3 are required, then do differentiation to find the first derivative. Then enter into Y1. Y2 and Y3 will then give the second and third derivative.

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