# Solve all Q11, 12, 13 explaining detailly each step Transcribed Image Text: 7x 2. The first three terms in an expansion

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+.Find the values of a and b 3. 14, The first three terms in the expansion of who 1-x are 1, -2x and 4x? respectively. Determine the value 1+kx of k and state the range of values of x for wch the expansion is valid. |

Solve all Q11, 12, 13 explaining detailly each step Transcribed Image Text: 7x

2.

The first three terms in an expansion of (l+bx)(1- ax) as a series in ascending powers of x are 1

and x. Given that a > 0, find the values of a and b.

3. When x and gher powers of x are neglected, (4 + ax) + (4 + ax) = b + 3x+ cx². Find the

values of the real constants a, b and c. state the range of values of x for wch the expansion is

ascending powers of x is valid.

CX

x+2

Given that g(x)=,x+ x* + 2x +2 and that f(x)

g(x)

expand f(x) as a series in ascending powers of

%3D

x up to and including the term x. Obtain also the range of values of x for wch the complete

expansion is valid. (NB. First show that x + 1 is a factor of g(x) and also express f(x) in partial

fractions)

12

3/ Find the term independent of x in the expansion of (x +-)

Expand (1 +x)as series of ascending powers of x as far as the term x”. By putting x 1/3 obtain

an approximation to V65 to 3 decimal places.

2 1/3

1–2x

V. Given that f(x) =

obtain the expansions of f(x) as a series of ascending powers of x up to and

V 1+4x

7

including the term in x’. Verify that f) =

2V13

Hence, use your expansion to obtain to 2 decimal places an approximate value for v13.

8. Expand (2+3x) in ascending powers of x up to and including the term in x. State the range of

values of x for wch the expansion is valid.

10

3

O Find the coefficient of x in the binomial expansion of

AGiven that gtx)=

express g(x) in partial fractions. Hence, or eherwise, obtain the first

(x-1)(x+1)’

three terms in the expansion of g(x) in ascending powers of x.

4. Show that if x is so smail that x and gher powers can be neglected, then:

= 1+x+xr?

2-3x

12 Given that: f(x)

express f(x) as a series in ascending powers of x, up to and including

(1-x)(2-x)

the term in x, giving the range of values of x for wch the expansion is valid.

ro. Given that (1+x 1

ax

3.

-bx² +.Find the values of a and b

3.

14, The first three terms in the expansion of

who

1-x

are 1, -2x and 4x? respectively. Determine the value

1+kx

of k and state the range of values of x for wch the expansion is valid.

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