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

Excerpt
+.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.