Page 174 - ADVANCED MATH F.5

Form Five Form Five

3. Guide students through discussion to deduce that Maclaurin’s
series is a special case of Taylor’s series when a = 0.
4. Use Examples 8.74 and 8.75 in the Student’s Book to guide
students to apply Maclaurin’s series to find solutions of the
9. 1− FOR ONLINE READING ONLY
given problems.

5. Assign students to attempt Exercise 8.18 in the Student’s Book.
Advise students to submit their work; check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 8.18

4 3 2 2 1 3
2. 5 + 5 x − 5 x − 10 x + 

64 1 1
x
3. (a) 4x − 8x + 2 x − 3 64x + 4  4. − <<
3 2 2
1  π 2 5  π   4
(b) 1+  x −  +  x −  + 
2  2  24  2 

(c) 2 − 2 x +   π  + 3   x + π   2 − 11   x + π   3 + 19   x + π    4 + 
 4  2  4  3 2  4  4 2  4 

1 3 1 1 1
(d) − x − x + 2 x + 3 x + 4 
2 2 4 4 3 48
1 1
5. (a) 1− x + 2 x + 4  (d) 1 2x+ − 2x + 2 4x − 3 10x + 4 
2! 4!
1
(b) x − x + 3 
3! 2 3 4
(c) 1+ (ln a x + ) (ln a ) x + 2 (ln a ) x + 3 (ln a ) x + 4 
2 6 24
16 128 3 9 9
6. 14θ − 2 θ + 4 θ − 6 +  7. 1+ x + x + 2 x + 3 
3 45 2 8 16
1 h + 2 1 h + 4 
2 24

168
Mathematics for Advanced Secondary Schools

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