core 4 partial fractions 4
DESCRIPTION
Designed for OCR A Level mathematics.TRANSCRIPT
Starter
2
3ln
32
)1(3ln
32
)1(3ln
32
1ln
32
2
1
1
32
2
1
1
)32)(1(
1
)32)(1(Find
lim
00
0
=
++
++=
++=
+−
+
+−
+≡
++
++
∞→
∫
∫∞
a
a
a
a
x
xdx
xx
xxxx
xx
dx
a
aa
Objective:
to find the series expansionof a rational function
Question 1
...235923
1817
...248)2(16
...1)1(
2
16
1
1
)2)(1(
1817
in term theasfar as 23
1817 ofexpansion series theFind
322
321
321
32
+−+−≡++
+
+−+−≡+
+−+−≡+
++
+≡
+++
+++
−
−
xxxxx
x
xxxx
xxxx
xxxx
x
xxx
x
Question 2
...2
113
)2)(12(
1212
...2
322)2(8
...421)12(
)2(
8
12
1
)2)(12(
1212
in term theasfar as x of powers ascendingin )2)(12(
1212 Expand
2
2
2
22
21
22
2
22
2
+−−≡+−+−
+−+−≡+−
+−−−≡−
+−
−≡
+−+−
+−+−
−
−
x
xx
xx
xxx
xxx
xxxx
xx
xxx
xx
C4 Textbook
Exercise 6D
Page 301
Questions 7 & 8
Misc Exercise 6
Page 311
Questions 16 & 17