y
-
3
-
2
!
-
I
4(x 1)
!
4
I
=
·
11
I
-
-
-
-
-
=
-
-
&
&
-
-
-
⑦
-
-
16(n 1) 1(3u + 2)
-
1
6(u2
1622
722
-
-
2n +
1)
-
324 + 16
gui + 124 + 4
1922 + 124 + 4
442 + 1210
nin
(7x
-
-
2)(x
-
6)10
En16
↓
-
Ms Hedy
-
8
amplitude
& D
n
can
>
>
-
be
(distance
found
between
2)
max & min
=
period
1288
·
600
down i
1200
transiti
·
↳
O
from
also
/
=
!
amplitude
a
Center
c
3
=
=
=
( 37
(2
-
2
3
-
=
=
AB
midpoint
=
radius
period
5
=
b
to find
,
-
,
6
1)
2) (
1)
1
+
=
-
0 +
49
v5
+
=
=
equation
:
(2 -2) + (y + 1)2
=
74
fir
-
Ms
.
Hedy
-
u =
-
z
+
p( z)
-
=
a) -) + 2( + ) + a) z) + 2
-
-a+ -
+ 2
at
=
2
a
=
16
a
=
4
-
24 +
②
out a
/
42
=
0
synthetic
method
1604
O
-
g
P(x)
0
d
+ 2
+ 2
x
=
=
Q =
14
(8x2 + 2)(2x + 1)
Bu + 2
Do
-
b2
0
-
-
>
-
No
roots
4aco
640
-
64
10
shown
fin
-
=
Ms
.
Hedy
-
2(x2 x) +
3
-
c[(x =) -]
2(x 1)
-
2(x
+
-
-
-
t
-
1)2
+
+
3
3
=
G
x
=
Y
-
!
,
E
2(x 2)
=
-
↓
↓
n
n
-
E
2(y
=
=
5
-
1)2 +
-
2(y
+
-
z)2
= (y-z)
-
..
·
f(x)
=
t
-
U
↳ choose () because
of
range
f"(u)1
↓
with
domain
of original
n
same
:
>
y ? I
range -
y
i
it
y
fin
-
Ms.
.
Hedy
-
Q2
>
-
15
+ 5
5
=
50
QuCos
(0
5
=
-
Q2
sing
=
=
Fan
=
-
=
=
=
-
Ente
a = 5
c
=
=
6
fix
-
Ms
.
Hedy
-
+
2
=
2x
1
+
E2tzet
7 +
24
=
2x2 + 3x +
1
g
=
2x2 + x
6
0
=
(2x
n
y
-
-
3)(u + 2)
2-
=
=
x = -
c(z)
+
1
:
y
=
4
A
(2
,
4)
↓
-
Ms.
.
Hedy
-
Area
of
shaded
=
Sycurve-yline
bottom
T
o
=
+ 2
(2x + 1)d
-
O
=j
+ 2
2x
-
-
1dn
3
=/
=
=
=
-
5(n(x + 1)
(5(n()
5(5
-
-
2n
-
x +
P
5/n2
di
+ 1
+
-
x)
3)
-
(0
-
0 +
0
2
Y
fo
-
Ms
.
Hedy
-
Geometric
Arithmetic
-
mu
Uz
=
ar
=
10r
Us
=
ar
=
10r
>
-
100
=
d =
>
-
10r2
d
2
10 + 3d
11
=
=
10 +
54
1
(4
=
a +
3d
=
10 + 3d
Vo
=
a +
5d
=
10 +
56
10.
&
50(r
5r
-
1)
-
30(r 1)
-
=
=
3r2
g
=
3r2
O
=
5
(3r
r =
d
=
-
-
-
3
54
+
2)(r
2
-
1)
z
-
I
r
Sum
=
to
infinity
achieved
when
Iul-I
f
-
Ms.
.
Hedy
-
-
logy(x + 1)
Subs
=
:
(0g (x 1)
,
+
=
p
(u 1)
+
·
pa
-
3p
-
4
(p 4)(p
-
P
>
-
log,(x
1)
+
n +1
x + 1
z
=
=
=
=
=
4
24
16
15
0
=
0
)
+
4 p
=
=
-
=
10gz(x 1)
+
n +1
x + 1
x
=
=
=
-
2-
t
-
=
1
t
logab
&
f
-
Ms .
Hedy
-
0
x =
5
y
-
=
=
(27) y
(33)
m
+
=
P(5 9)
,
Normal
y
=
g =
-
y
,
a+
+
= (5x
+
-
(5)
-
=
=
2
+
P(5 9)
=.
=
+
qx
.
5
subs =
5
3
-
=.
,
5
2)
P to the curve
=
Mr
-
c
⑦
c
The
intersects
line
normal
n +
y
=
Q
at
11
E
1x0
+
n
27
-
2)
= (27)
mx + C
9 =
c
T
at
-
z(5u
=
Mr
Line
Mu =
y
9
=
③
(5x + 2)
=
+
7
102
-
gn
+
+
=
135
=
x
=
y
=
110
-
25
=
11 + 25
=
34
Q( 25 34)
-
②
Imagine
,
tangent
normal
So
the
midpoint
,
So -
R
P is
/
P(5 9)
of
5
Q(-25 34) R(x y)
,
,
E-10
=
,
,
-25 +
=
u = 35
9
R
=
4
34
+
-
y
:
R
(35
,
34 + y
10 =
=
-
16
-16)
fix
-
Ms .
Hedy
-
ta
7
3d
7
X
B
=
bi
[b
II
>
+
BX
>
-
*
EN
>
=
G + ON
-
=
b
+
=
b
+
=
=
b
(1
-
-
-
X BN
=
b
+
ga
x) b ya)
+
-
xb
x)b
+
qxa
+
qxa
T
fix
-
Ms
.
Hedy
-
x
On
=
+
M
=
(b + M) 2b
-
=
(1
-
=
-b - mb
=
(2
from
x(b
coefficient
-
=
+ xa
=
-b +
a
a)
Ma
ma
@
(t
from (b)
-
EM)b
+
Ma
be
n
coefficient
+
+
Em)b +
(a)
T + F
=
MMA
=b +
X
MA
*
a
-
-
2x
=
x
=
- 1
m
....
....
(1)
(2)↑
sub
Ex
-
-
2x
Ex
x
=
=
1
-
-
1
=
/
M =
1x
l =
3
T
fix
-
Ms
.
Hedy
-
Hv + 4v
-4
1
1
=
e
.
v
3x + 2
934
+
x
+
3n e
.
+ 2
3
.
dx
32 + 2
=
e
32 + 2
Y
Reverse
((e3u
of
process
+ 2
+
3xe
su +
derivative
2) du
>
-
ve3u
=
integral
+ 2
t
c
now
modify
-
separate
Sebuthda
See
+
>
32 + 2
+
Jueute
de
=
see
+
du= -lebutt
more
~
+
Jeenth de =
but
-+
=
t
f
-
Ms
.
Hedy
-