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Physics & Maths TutorTypewritten TextEdexcel Maths C4

Physics & Maths TutorTypewritten TextTopic Questions from Papers

Physics & Maths TutorTypewritten TextBinomial Expansion

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2

1. Use the binomial theorem to expand

in ascending powers of x, up to and including the term in x3, simplifying each term.

(5)

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4(4 9 ), | | ,

9x x

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10

5.

(a) Find the values of A and C and show that B = 0. (4)

(b) Hence, or otherwise, find the series expansion of f(x), in ascending powers of x, upto and including the term in x3. Simplify each term.

(7)

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2132 2

3 16f ( ) , | | .(1 3 )(2 ) (1 3 ) (2 ) (2 )

x A B Cx xx x x x x

*N23553A01020*

physicsandmathstutor.com January 2006

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4

2.

Given that, for where A and B are constants,

(a) find the values of A and B.(3)

(b) Hence, or otherwise, find the series expansion of f(x), in ascending powers of x, upto and including the term in x3, simplifying each term.

(6)

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2 2

3 1 ,(1 2 ) (1 2 ) (1 2 )

x A Bx x x

= +

12,x

122

3 1f ( ) , | | .(1 2 )

xx xx

=