*: Not in topics tested for 2014 SRJC Promo

1* (i) Find the expansion of 21

(4 2 )x

x

+

+ in ascending powers of x, up to and including the

term in 2x . [3]

(ii) State the range of values of x for which this expansion is valid. [1]

(iii) Write down the equation of the tangent to the curve 21

(4 2 )xy

x

+= +

at the point where x = 0. [1]

1(i)

( )( )( )( )( )

2

12 2

122

22

2 2

2 2

2

1(4 2 )

1 4 2

1 1 12 2

1 31 1 2 21 1 ...2 2 2 2! 2

1 31 1 ...2 4 321 1 3 1

...

2 8 64 21 1 35

...

2 8 64

x

x

x x

xx

x xx

xx x

x x x

x x

+

+= + +

= + +

= + + + +

= + + +

= + + +

= + +

(ii) 1

2

1 12

2 2

x

x

x