All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)

(a)

When

(b)

Using the Graphing Calculator,

The approximation is not very good since is not very close to zero.

We only considered up to , thus the approximation can be improved by taking into consideration more terms.

### KS Comments:

Just don’t be careless for (i)! Some students still can be unsure of how to evaluate a definite integral using Graphing Calculator. Lastly, maclaurin’s series expansion are most accurate when value is close to one since they are centred at x = 0.

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