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.

Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline.


Click Here to Make an Order Click Here to Hire a Writer