Choosing a suitable value for binomial approximation


Example 1



If the expansion is of other forms, can try the method shown in example 2.

Example 2

Suppose you are asked to expand Tex2Img_1396431523 using binomial expansion, then use the results to approximate Tex2Img_1396431669

How do you select a suitable value for the approximation?

Step 1

Make sure the value selected is within the range of values for which the expansion is valid. In this example, the valid range is from -4 to 4.

Step 2

4-x = (13 / perfect square) or (perfect square/13)

So 4-x = (13 /4 or 13/9) or (49/13)

x= 3/13 or 3/4 or 23/9

Choose the smallest value 3/13 as value closer to 0 gives better approximation.

Therefore, Capture

LHS can be approximated using the binomial expansion. Hence Tex2Img_1396431669 can be approximated.

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