10. Express- in partial fractions. Use the substitutions t = tan x to show that (3t+1)(t+3) dt. Hence, show that: Jo 3+5sin2x dx = -In3. Jo 3+5sin2x (3t+1)(y+3) d honce show that * f(x)d:
10. Express- in partial fractions. Use the substitutions t = tan x to show that (3t+1)(t+3) dt. Hence, show that: Jo 3+5sin2x dx = -In3. Jo 3+5sin2x (3t+1)(y+3) d honce show that * f(x)d:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 83E
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Solve Q10, & 11 showing clearly all steps involved
Transcribed Image Text:in partial fractions, and hence expand this function in a series of ascending powers
9. Express
(x+2)(x-1)
of x as far as the term in x. Determine the set of values of x for which the expansion is valid.
%3D
1
in partial fractions. Use the substitutions t= tan x to show that
10. Express
(3t+1)(t+3)
dx =-In3.
8
1
dt. Hence, show that: 4
1
0 3+5sin2x
4.
ニ
0 3+5sin2x
(3t+1)(y+3)
3 t
x+x?
in partial fractions and hence show that f(x)dx
20
11. Express f(x), where f(x)
13 In2
(x²+1)(x-2)
10
5x+3
2 12. Express f(x) =
in partial fractions.
(1+3x)(1+x)
2
13. Express
in partial fractions. Hence solve the differential equation:
(1+x)(1+3x)
dy
2(y+2)
given that y = -1 when x = 0.
dx
(1+x)(1+3x)'
14. Given that g(x) =
(1+x)(1+3x²)’
a. Express g(x) in partial fractions, hence
b. Evaluate g(x)dx,
c. Expand g(x) as a series in ascending powers of x, up to and including the term in x'.
6x + 1
6x+1
15. Express
in partial fractions, hence prove that
,
2 (2x-3)(3x-2)
dx = In 10
(2x – 3)(3x – 2)
1
16. Express
into partial fractions.By using the substitution t = tan x, or otherwise show
(3t+1)(t+1)
TT
dx
that 3+5sin 2x
= In 2.
||
X-1
17. Express f(x)
into partial fractions. Hence or otherwise obtain the first three terms of the
(x+1) (x-3)
binomial expansion of (fx), stating the range of values of x for which the expansion is valid.
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