| File: |
TortureTests/Complexity/complex300.xml |
| Author: |
Mackichan Software (S. Swanson) |
| Description: |
Around 300 equation tests. Red coloring added in markup. |
| Sample Rendering: |
N/A
|
Your browser's rendering:
M1
2
⁢
∑
a
⁢
b
M2
x
′
3
M3
f
′
⁡
(
x
)
+
sin
⁡
cos
⁡
θ
=
1
M4
f
⁡
(
z
)
=
∑
n
=
0
∞
a
n
⁢
z
n
,
|
z
|
<
R
⁣
(
R
≠
0
)
M5
∫
C
(
∑
n
=
0
∞
a
n
⁢
z
n
)
⁢
ⅆ
z
=
∑
n
=
0
∞
a
n
⁢
∫
C
z
n
⁢
ⅆ
z
M6
lim
n
→
∞
|
∫
C
[
f
⁡
(
z
)
−
∑
k
=
0
n
a
k
⁢
z
k
]
⁢
ⅆ
z
|
=
0
M7
n
≥
N
⁡
(
ε
)
⇒
|
f
⁡
(
z
)
−
∑
k
=
0
n
a
k
⁢
z
k
|
<
ε
M8
10
 Bq
+
10
 Ci
M9
10
 amol
+
10
 Emol
−
10
 fmol
+
10
 Gmol
−
10
 kmol
+
10
 Mmol
M10
10
 μmol
+
10
 mmol
−
10
 mol
+
10
 nmol
−
10
 Pmol
+
10
 pmol
−
10
 Tmol
M11
10
 acre
+
10
 hectare
−
10
 ft
2
+
10
 in
2
−
10
 m
2
M12
10
 A
+
10
 kA
−
10
 μA
+
10
 mA
−
10
 nA
M13
10
 F
+
10
 μF
−
10
 mF
+
10
 nF
−
10
 pF
M14
10
 C
+
1.0
 m/s/s
−
0.1
 m
/
s
2
M15
10
 kS
+
10
 μS
−
10
 mS
+
10
 S
M16
10
 kV
+
10
 MV
−
10
 μV
+
10
 mV
−
10
 nV
+
10
 pV
−
10
 V
M17
10
 GΩ
+
10
 kΩ
−
10
 MΩ
+
10
 mΩ
−
10
 Ω
M18
10
 Btu
+
10
 cal
−
10
 eV
+
10
 erg
−
10
 GeV
+
10
 GJ
M19
10
 J
+
10
 kcal
−
10
 kJ
+
10
 MeV
−
10
 MJ
+
10
 μJ
−
10
 mJ
+
10
 nJ
M20
10
 dyn
+
10
 kN
−
10
 MN
+
10
 μN
−
10
 mN
+
10
 N
−
10
 ozf
+
10
 lbf
M21
10
 EHz
+
10
 GHz
−
10
 Hz
+
10
 kHz
−
10
 MHz
+
10
 PHz
−
10
 THz
M22
10
 fc
+
10
 lx
−
10
 phot
M23
10
 Å
+
10
 am
−
10
 cm
+
10
 dm
−
10
 fm
+
10
 ft
−
10
 in
M24
10
 km
+
10
 m
−
10
 μm
+
10
 mi
−
10
 mm
+
10
 nm
−
10
 pm
M25
10
 sb
M26
10
 lm
M27
10
 cd
M28
10
 Mx
+
10
 μWb
−
10
 mWb
+
10
 nWb
−
10
 Wb
M29
10
 G
+
10
 μT
−
10
 mT
+
10
 nT
−
10
 pT
+
10
 T
M30
10
 H
+
10
 μH
−
10
 mH
M31
10
 u
+
10
 cg
−
10
 dg
+
10
 g
−
10
 kg
+
10
 μg
−
10
 mg
+
10
 lb
−
10
 slug
M32
10
 °
+
10
 μrad
−
10
 mrad
+
10
​
′
−
10
 rad
+
10
​
′′
M33
10
 GW
+
10
 hp
−
10
 kW
+
10
 MW
−
10
 μW
+
10
 mW
−
10
 nW
+
10
 W
M34
10
 atm
+
10
 bar
−
10
 kbar
+
10
 kPa
−
10
 MPa
+
10
 μPa
−
10
 mbar
+
10
 mmHg
−
10
 Pa
+
10
 torr
M35
10
 sr
M36
10
 °C
+
10
 °F
−
10
 K
M37
10
 as
+
10
 d
−
10
 fs
+
10
 h
−
10
 μs
+
10
 ms
−
10
 min
+
10
 ns
−
10
 ps
+
10
 s
−
10
 y
M38
10
 ft
3
+
10
 in
3
−
10
 m
3
+
10
 gal
−
10
 l
M39
10
 ml
+
10
 pint
−
10
 qt
M40
1
x
⁡
(
y
)
=
(
−
∫
e
−
1
2
⁢
y
2
⁢
sin
⁡
y
⁢
ⅆ
y
+
C
1
)
⁢
e
1
2
⁢
y
2
M41
ⅅ
x
y
−
y
=
sin
⁡
x
M42
(
1
2
)
⁢
(
1
2
)
⁢
(
1
2
)
M43
[
1
2
]
⁢
(
1
2
)
⁢
{
1
2
}
M44
⟨
1
2
⟩
⁢
⌊
1
2
⌋
⁢
⌈
1
2
⌉
M45
↑
1
2
↑
⁢
↓
1
2
↓
⁢
↕
1
2
↕
M46
1
2
⁢
1
2
⁢
1
2
M47
1
2
⁢
1
2
⁢
1
2
M48
1
2
⁢
1
2
⁢
1
2
M49
−
(
a
−
b
)
=
b
−
a
M50
2
5
+
3
7
=
2
⋅
7
+
3
⋅
5
35
=
29
35
M51
|
a
|
=
{
a
if
a
≥
0
−
a
if
a
<
0
M52
a
n
=
a
⋅
a
⋅
⋯
⋅
a
⏟
n
factors
M53
(
a
b
)
−
n
=
(
b
a
)
n
M54
a
n
=
b
means
b
n
=
a
.
M55
16
81
4
=
16
4
81
4
=
2
3
M56
{
x
∣
x
≠
0
,
x
≠
1
}
M57
a
n
⁢
x
n
+
a
n
−
1
⁢
x
n
−
1
+
⋯
+
a
1
⁢
x
+
a
0
M58
a
3
−
b
3
=
(
a
−
b
)
⁢
(
a
2
+
a
⁢
b
+
b
2
)
M59
(
x
+
y
)
2
M60
H
=
{
(
a
b
c
d
)
∈
G
∣
a
⁢
d
−
b
⁢
c
=
1
}
M61
|
x
|
+
||
y
||
+
{
z
}
−
[
a
⁢
c
]
+
(
b
)
=
[
a
,
b
]
M62
x
=
1
M63
x
=
1
M64
x
=
1
M65
x
=
1
M66
[
−
10
3
,
−
7
3
)
∪
(
−
7
3
,
−
4
3
]
M67
A
⁢
∂
u
∂
x
+
B
⁢
∂
u
∂
y
+
C
⁢
u
=
E
M68
∑
​
​
x
M69
∑
1
<
i
<
10
1
<
j
<
10
​
2
i
+
j
M70
Γ
1
2
3
4
​
5
6
7
​
​
1
5
7
6
2
4
3
M71
y
⁡
(
x
)
=
x
⁢
e
x
−
e
x
+
2
e
x
=
x
−
1
+
2
e
x
M72
ⅅ
x
⁣
x
y
−
y
=
0
y
⁡
(
0
)
=
1
y
′
⁡
(
0
)
=
0
M73
y
⁡
(
x
)
=
1
3
⁢
e
−
(
−
1
)
3
⁢
x
+
2
3
⁢
e
1
2
⁢
(
−
1
)
3
⁢
x
⁢
cos
⁡
1
2
⁢
3
⁢
(
−
1
)
3
⁢
x
M74
y
⁡
(
t
)
=
2
⁢
tan
⁡
(
2
⁢
t
−
1
4
⁢
π
)
M75
ℱ
⁡
(
e
2
⁢
π
⁢
i
⁢
x
2
⁢
π
⁢
Dirac
⁡
(
x
−
2
⁢
π
)
,
x
,
s
)
=
(
2
⁢
π
⁢
Dirac
⁡
(
s
−
2
⁢
π
)
2
⁢
π
⁢
e
−
2
⁢
i
⁢
π
⁢
s
)
M76
x
=
1
x
+
3
=
123
M77
t
x
y
z
0
1.0000
1.0000
1.0000
.1
1.1158
1.0938
.8842
.2
1.2668
1.1695
.7332
.3
1.4582
1.2173
.5418
.4
1.6953
1.2253
.3047
.5
1.9830
1.1791
.0170
.6
2.3256
1.0619
−
.3256
.7
2.7265
.8542
−
.7265
.8
3.1873
.5344
−
1.1873
.9
3.7077
.0777
−
1.7077
1.0
4.2842
−
.5424
−
2.2842
M78
K
v
⁡
(
z
)
=
BesselK
v
⁡
(
z
)
M79
z
2
⁢
ⅆ
2
w
ⅆ
z
2
+
z
⁢
ⅆ
w
ⅆ
z
−
(
z
2
+
v
2
)
⁢
w
=
0
M80
∂
2
u
⁡
(
x
,
y
)
∂
x
2
−
∂
2
u
⁡
(
x
,
y
)
∂
y
2
=
0
M81
y
⁡
(
t
,
x
)
=
F
1
⁢
(
−
x
−
a
⁢
t
)
+
F
2
⁢
(
x
−
a
⁢
t
)
M82
1
2
3
4
5
6
M83
2
⁢
x
+
1
=
5
M84
1
=
3
9
=
7
M85
a
⁢
b
c
⁢
d
e
⁢
f
M86
x
+
2
⁢
y
−
3
=
5
4
⁢
x
−
y
−
5
=
98
M87
x
=
z
1
=
3
M88
A
1
=
N
0
⁡
(
λ
;
Ω
′
)
−
φ
⁡
(
λ
;
Ω
′
)
,
A
2
=
φ
⁡
(
λ
;
Ω
′
)
−
φ
⁡
(
λ
;
Ω
)
,
A
3
=
N
⁡
(
λ
;
ω
)
.
M89
sin
⁡
θ
cos
⁡
γ
M90
x
=
{
x
if
x
<
0
−
x
if
x
≥
0
M91
L
⁢
M
⁢
R
⁢
M
L
⁢
M
⁢
R
⁢
M
M92
M
⁢
A
⁢
T
⁢
H
M
⁢
A
⁢
T
⁢
H
M93
M94
⋮
M95
∇×
F
=
0
M96
∇·
F
M97
∇·∇
F
=
∇
2
F
+
7
=
A
M98
∇×
(
x
⁢
y
,
y
⁢
z
,
z
⁢
x
)
=
[
−
y
−
z
−
x
]
M99
∇×
(
y
,
z
,
x
)
=
(
−
1
,
−
1
,
−
1
)
≠
0
M100
x
+
y
+
α
=
102
M101
a
+
b
=
c
M102
x
+
1
M103
x
+
f
⁡
(
x
)
−
1
=
123
M104
T
⁢
h
⁢
e
⁢
q
⁢
u
⁢
i
⁢
c
⁢
k
⁢
b
⁢
r
⁢
o
⁢
w
⁢
n
⁢
f
⁢
o
⁢
x
⁢
j
⁢
u
⁢
m
⁢
p
⁢
s
⁢
o
⁢
v
⁢
e
⁢
r
⁢
t
⁢
h
⁢
e
⁢
l
⁢
a
⁢
z
⁢
y
⁢
d
⁢
o
⁢
g
.
T
⁢
h
⁢
e
⁢
e
⁢
n
⁢
d
.
M105
(
∂
f
∂
x
1
⁡
(
c
1
,
c
2
,
…
,
c
n
)
,
∂
f
∂
x
2
⁡
(
c
1
,
c
2
,
…
,
c
n
)
,
…
,
∂
f
∂
x
n
⁣
1
⁡
(
c
1
,
c
2
,
…
,
c
n
)
)
M106
∇
(
c
⁢
u
⁢
v
+
v
2
⁢
w
)
=
(
u
⁢
v
,
c
⁢
v
,
c
⁢
u
+
2
⁢
v
⁢
w
,
v
2
)
M107
D
u
⁢
f
⁡
(
a
,
b
,
c
)
=
∇
f
⁡
(
a
,
b
,
c
)
⋅
u
=
∂
f
∂
x
⁡
(
a
,
b
,
c
)
⁢
u
1
+
∂
f
∂
y
⁡
(
a
,
b
,
c
)
⁢
u
2
+
∂
f
∂
z
⁡
(
a
,
b
,
c
)
⁢
u
3
M108
θ
∈
{
π
+
2
⁢
X
3
⁢
π
−
(
arccos
⁡
1
7
⁢
14
)
|
X
3
∈
ℤ
}
,
θ
∈
{
2
⁢
X
4
⁢
π
−
π
+
(
arccos
⁡
1
7
⁢
14
)
|
X
4
∈
ℤ
}
M109
P
=
A
⁢
(
A
T
⁢
A
)
−
1
⁢
A
T
M110
det
(
x
y
1
a
b
1
a
d
1
)
=
x
⁢
b
−
x
⁢
d
+
a
⁢
d
−
a
⁢
b
=
0
M111
A
⁡
(
θ
)
⁢
A
⁡
(
−
θ
)
=
[
cos
⁡
θ
−
sin
⁡
θ
sin
⁡
θ
cos
⁡
θ
]
⁢
[
cos
⁡
θ
sin
⁡
θ
−
sin
⁡
θ
cos
⁡
θ
]
M112
J
⁡
(
A
)
=
[
J
n
1
⁡
(
λ
1
)
0
⋯
0
0
J
n
2
⁡
(
λ
2
)
⋯
0
⋮
⋮
⋱
⋮
0
0
⋯
J
n
k
⁡
(
λ
k
)
]
M113
det
(
−
4
+
X
−
1
0
0
−
4
+
X
0
0
0
−
4
+
X
)
=
(
X
−
4
)
3
M114
{
(
−
1
2
−
1
6
⁢
33
1
)
}
↔
5
2
−
1
2
⁢
33
M115
∥
A
∥
=
max
x
≠
0
∥
A
⁢
x
∥
∥
x
∥
M116
(
a
1
⁣
1
a
1
⁣
2
a
2
⁣
1
a
2
⁣
2
)
+
(
b
1
⁣
1
b
1
⁣
2
b
2
⁣
1
b
2
⁣
2
)
=
(
a
1
⁣
1
+
b
1
⁣
1
a
1
⁣
2
+
b
1
⁣
2
a
2
⁣
1
+
b
2
⁣
1
a
2
⁣
2
+
b
2
⁣
2
)
M117
f
⁡
(
[
1
2
4
3
]
)
=
[
1
2
4
3
]
2
−
5
⁢
[
1
2
4
3
]
−
2
=
[
2
−
2
−
4
0
]
M118
x
=
lim
x
=
1
∑
1
2
a
M119
∫
a
b
f
⁡
(
x
)
⁢
ⅆ
x
=
lim
∥
P
∥
→
0
∑
i
=
1
n
f
⁡
(
x
‾
i
)
⁢
Δ
x
i
M120
∫
a
b
f
⁡
(
x
)
⁢
ⅆ
x
=
lim
n
→
∞
b
−
a
n
⁢
∑
i
=
1
n
f
⁡
(
a
+
i
⁢
b
−
a
n
)
M121
∫
0
2
x
5
⁢
x
3
+
1
⁢
ⅆ
x
=
∫
1
3
2
3
⁢
u
⁢
(
u
2
)
(
u
2
−
1
)
2
3
⁢
(
u
2
⁢
(
u
2
−
1
)
2
3
−
(
u
2
−
1
)
2
3
)
⁢
ⅆ
u
M122
∫
f
⁡
(
g
⁡
(
x
)
)
⁢
g
′
⁡
(
x
)
⁢
ⅆ
x
=
∫
f
⁡
(
u
)
⁢
ⅆ
u
M123
x
=
2
⁢
∑
n
=
1
100
n
⁢
(
n
−
1
)
M124
lim
x
→
0
sin
⁡
(
1
x
)
=
−
1
..
1
M125
h
⁡
(
i
,
j
)
=
(
2
−
j
)
⁢
g
⁡
(
i
)
+
(
j
−
1
)
⁢
f
⁡
(
g
⁡
(
i
)
)
M126
△
:
[
0
,
1
]
→
[
0
,
1
]
M127
0
▽
x
=
x
M128
x
△
y
=
h
−
1
⁢
(
h
⁡
(
x
)
⁢
h
⁡
(
y
)
)
M129
x
△
y
=
f
−
1
⁢
(
max
{
f
⁡
(
x
)
+
f
⁡
(
y
)
−
1
,
0
}
)
M130
x
▽
y
=
η
⁡
(
η
⁡
(
x
)
△
η
⁡
(
y
)
)
M131
x
⁢
△
0
y
=
{
x
∧
y
if
x
∨
y
=
1
0
if
x
∨
y
<
1
M132
lim
a
→
1
+
log
a
⁡
[
1
+
(
a
x
−
1
)
⁢
(
a
y
−
1
)
a
−
1
]
=
lim
a
→
1
−
log
a
⁡
[
1
+
(
a
x
−
1
)
⁢
(
a
y
−
1
)
a
−
1
]
=
x
⁢
y
M133
g
⁡
(
x
)
=
exp
⁡
(
−
1
−
(
1
−
x
)
a
(
2
a
−
1
)
⁢
(
1
−
x
)
a
)
M134
Aut
(
I
)
=
{
f
:
[
0
,
1
]
→
[
0
,
1
]
|
f
is one-to-one and onto, and
x
≤
y
implies
f
⁡
(
x
)
≤
f
⁡
(
y
)
}
M135
x
2
+
y
2
=
r
2
,
tan
⁡
θ
=
y
x
M136
2
⁢
1
−
t
2
M137
[
(
2
+
sin
⁡
t
)
⁢
10
⁢
cos
⁡
t
,
(
2
+
cos
⁡
t
)
⁢
10
⁢
sin
⁡
t
,
3
⁢
sin
⁡
3
⁢
t
]
M138
{
t
=
0
,
s
=
0
}
,
{
t
=
π
,
s
=
π
}
M139
1
2
3
4
5
6
7
8
9
10
2
4
6
8
10
1
3
5
7
9
3
6
9
1
4
7
10
2
5
8
4
8
1
5
9
2
6
10
3
7
5
10
4
9
3
8
2
7
1
6
6
1
7
2
8
3
9
4
10
5
7
3
10
6
2
9
5
1
8
4
8
5
2
10
7
4
1
9
6
3
9
7
5
3
1
10
8
6
4
2
10
9
8
7
6
5
4
3
2
1
M140
testing
x
2
end.
M141
x
M142
x
M143
x
M144
x
M145
ⅆ
f
ⅆ
x
⁡
(
x
1
)
=
5
M146
∫
x
⁢
ⅆ
x
=
∬
x
⁢
y
⁢
ⅆ
x
⁢
ⅆ
y
=
∭
x
⁢
y
⁢
z
⁢
ⅆ
x
⁢
ⅆ
y
⁢
ⅆ
z
=
⨌
x
⁢
y
⁢
z
⁢
t
⁢
ⅆ
x
⁢
ⅆ
y
⁢
ⅆ
z
⁢
ⅆ
t
M147
mod
a
M148
5
mod
3
=
2
M149
f
⁡
(
0
)
mod
3
=
1
M150
5
⁢
x
+
4
≡
8
⁣
(
mod
13
)
M151
a
=
(
5
−
3
)
/
5
mod
7
=
6
M152
(
2
⁢
x
2
+
x
+
2
)
+
(
2
⁢
x
+
1
)
mod
3
=
2
⁢
x
2
M153
+
0
1
000
000
111
1
1
0
M154
4. 974 9
M155
ⅆ
ⅆ
x
F
⁡
(
x
)
M156
[
86.333
,
146.33
,
129.33
]
M157
BinomialDist
⁡
(
x
;
n
,
p
)
=
∑
k
=
0
x
(
n
k
)
⁢
p
k
⁢
q
n
−
k
M158
Pr
(
X
≤
54
)
=
BinomialDist
⁡
(
54
;
100
,
.55
)
=
.45846
M159
k
=
max
{
|
∂
f
∂
y
⁡
(
x
,
y
)
|
:
(
x
,
y
)
∈
D
}
.
M160
m
=
lim
x
→
a
f
⁡
(
x
)
−
f
⁡
(
a
)
x
−
a
M161
|
A
|
=
|
a
1
⁣
1
a
1
⁣
2
⋅
⋅
⋅
a
1
⁣
n
a
2
⁣
1
a
2
⁣
2
⋅
⋅
⋅
a
2
⁣
n
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
a
n
⁣
1
a
n
⁣
2
⋅
⋅
⋅
a
n
⁣
n
|
=
a
1
⁣
1
⁢
A
1
⁣
1
+
a
1
⁣
2
⁢
A
1
⁣
2
+
⋯
+
a
1
⁣
n
⁢
A
1
⁣
n
M162
x
=
1
(
hl text
x
end.
)
M163
x
=
1
(
hl to URI
x
end
)
M164
x
=
1
(
sex
)
M165
x
=
1
(
jbm
)
M166
M167
f
⁡
(
x
)
⁢
g
⁢
[
y
]
⁢
h
⁢
{
z
}
+
⌊
a
⌋
⁢
⌈
b
⌉
⁢
⟨
c
⟩
M168
123
456
A
|
∥
A
B
A
/
1
2
A
/
⁢
(
3
4
A
)
↕
5
6
A
↕
7
8
A
⇕
9
20
10
A
⇕
↑
11
12
A
↑
⁢
⇑
13
14
A
⇑
↓
15
16
A
↓
⇓
17
18
A
⇓
M169
x
⁢
x
x
x
x
⁢
x
M170
(
a
1
,
a
2
,
…
,
a
n
)
⋅
(
b
1
,
b
2
,
…
,
b
n
)
=
a
1
⁢
b
1
*
+
a
2
⁢
b
2
*
+
⋯
+
a
n
⁢
b
n
*
M171
⌊
n
5
⌋
+
⌊
n
5
2
⌋
+
⌊
n
5
3
⌋
+
⌊
n
5
4
⌋
+
⋯
M172
x
1
+
⋯
+
x
n
M173
x
+
⋯
+
x
⏟
k
times
M174
x
1
⁢
x
2
⁢
⋯
⁢
x
n
n
M175
n
!
=
1
×
2
×
3
×
4
×
⋯
×
n
M176
P
:
a
=
x
0
<
x
1
<
x
2
<
⋯
<
x
n
=
b
M177
f
⁡
(
x
)
=
30
13
⁢
cos
⁡
x
+
10
3
⁢
(
100
+
9
cos
2
⁡
x
−
60
cos
⁡
x
⁢
sin
⁡
(
x
+
29
90
⁢
π
)
)
M178
∫
cos
⁡
(
A
⁢
x
)
⁢
sin
⁡
(
B
⁢
x
)
⁢
ⅆ
x
=
−
cos
⁡
(
B
−
A
)
⁢
x
2
⁢
(
B
−
A
)
+
−
cos
⁡
(
B
+
A
)
⁢
x
2
⁢
(
B
+
A
)
+
C
.
M179
235.3
+
813
=
1048. 3
M180
max
−
2
≤
x
≤
2
(
x
3
−
6
⁢
x
+
3
)
=
8.0
M181
x
⁢
decade
=
2
⁢
century
M182
ⅆ
5
(
x
7
−
3
⁢
x
6
)
ⅆ
x
5
ⅆ
n
sin
⁡
x
ⅆ
x
n
ⅆ
3
ⅆ
x
3
f
⁡
(
x
)
ⅆ
2
ⅆ
t
2
(
4
⁢
t
5
−
3
⁢
t
)
M183
f
⁡
(
x
)
=
30
13
⁢
cos
⁡
x
+
10
3
⁢
(
100
+
9
cos
2
⁡
x
−
60
cos
⁡
x
⁢
sin
⁡
(
x
+
29
90
⁢
π
)
)
M184
∫
R
3
(
|
u
1
|
2
+
|
∇
u
0
|
2
2
+
|
u
0
|
6
6
)
⁢
ⅆ
x
<
∞
M185
(
∇×
F
)
⋅
k
=
z
+
1
M186
M
⁢
M
M
M
M
M187
ⅅ
x
x
2
ⅅ
x
(
x
2
)
ⅅ
x
⁣
x
(
x
2
)
ⅅ
x
2
(
x
2
)
ⅅ
x
⁣
y
(
x
2
⁢
y
3
)
ⅅ
x
s
⁣
y
t
(
x
2
⁢
y
3
)
M188
5
24
!
x
6
M189
x
+
a
y
−
1
12.34
2
sin
⁡
θ
1
M190
0
1
1
0
M191
(
0
−
i
i
0
)
M192
[
1
0
0
−
1
]
M193
|
a
b
c
d
|
M194
∥
1
0
1
0
11
∥
M195
1
2
3
4
5
M196
testing
sin
⁡
θ
M197
a
^
+
b
ˇ
+
c
˜
+
d
´
+
e
`
+
f
˘
+
g
¯
+
h
+
i
˚
+
j
˙
+
k
¨
+
l
⃛
+
m
⃜
+
n
→
M198
f
⁡
(
g
⁡
(
x
)
)
=
sin
3
⁡
x
2
+
sin
⁡
x
2
⁢
sin
⁡
(
sin
⁡
x
2
)
M199
(
x
2
+
12
x
2
+
12
)
+
1234
M200
x
=
1
not
here
x
2
merged
y
1
jbm
lowlife
The end.
M201
x
2
+
y
2
=
z
2
−
1
M202
x
2
+
y
2
=
z
2
−
1
x
+
y
3
=
z
3
M203
x
2
+
y
2
=
z
2
−
1
x
+
y
3
=
z
3
M204
x
2
+
y
2
=
1
x
=
1
−
y
2
M205
(
a
+
b
)
2
=
a
2
+
2
⁢
a
⁢
b
+
b
2
(
a
+
b
)
⋅
(
a
−
b
)
=
a
2
−
b
2
M206
First line of equation
Middle line of equation
Other middle line of equation
Last line of equation
M207
L
1
=
R
1
L
2
=
R
2
L
3
=
R
3
L
4
=
R
4
M208
(
a
+
b
)
4
=
(
a
+
b
)
2
⁢
(
a
+
b
)
2
=
(
a
2
+
2
⁢
a
⁢
b
+
b
2
)
⁢
(
a
2
+
2
⁢
a
⁢
b
+
b
2
)
=
a
4
+
4
⁢
a
3
⁢
b
+
6
⁢
a
2
⁢
b
2
+
4
⁢
a
⁢
b
3
+
b
4
M209
x
2
+
y
2
=
1
x
=
1
−
y
2
(
a
+
b
)
2
=
a
2
+
2
⁢
a
⁢
b
+
b
2
(
a
+
b
)
⋅
(
a
−
b
)
=
a
2
−
b
2
M210
Vertex
V
⁡
(
0
,
0
)
Focus
F
⁡
(
0
,
p
)
Directrix
y
=
−
p
M211
ⅆ
ⅆ
x
  
(
csc
−
1
⁡
x
)
=
−
1
|
x
|
⁢
x
2
−
1
M212
tanh
−
1
⁡
x
=
1
2
⁢
ln
⁡
(
1
+
x
1
−
x
)
−
1
<
x
<
1
M213
∠
α
+
∠
A
B
C
+
∠
1
=
▵
a
b
c
M214
y
=
e
−
∫
P
⁢
ⅆ
x
⁢
[
∫
e
∫
P
⁢
ⅆ
x
⁢
Q
⁢
ⅆ
x
+
c
]
M215
x
=
1
+
y
3
and
x
=
1
+
y
M216
$
1.00
+
25
¢
−
3
£
+
2.45
¤
−
0.7
¥
−
a
₠
+
20
₣
+
30
₤
−
4.56
₧
M217
2
⁢
x
+
y
=
3
3
⁢
x
−
4
⁢
y
=
5
a
+
b
=
c
+
12345
M218
Unrestricted
Symmetric
Antisymmetric
Triangular
M219
a
≠
b
≠
x
M220
c
≮
d
≮
y
M221
e
≯
f
≯
11
M222
g
∉
h
∉
Z
M223
k
≁
l
≁
3
M224
A
⊄
B
⊂
C
M225
A
⫅̸
B
⊈
C
M226
10
≢
11
≡
12
M227
x
≰
y
≰
z
M228
lim
‾
x
M229
lim
_
x
M230
lim
→
x
M231
lim
←
x
M232
x
=
y
+
z
=
k
+
m
M233
College Algebra
Second Edition
James Stewart
McMaster Universitiy
Lothar Redlin
Pennsylvania State University
Saleem Watson
California State University, Long Beach
Copyright 1996, ISBN 0 534-33983-2
Brooks/Cole Publishing Company
An International Thomson Publishing Company
M234
{
1
2
1
2
↑
∑
1
2
}
M235
⟨
1
2
1
2
|
∑
1
2
⟩
M236
⌈
1
2
1
2
|
∑
1
2
⌉
M237
⇓
1
2
1
2
↕
∑
1
2
⇓
M238
[
1
2
1
2
]
M239
(
1
2
1
2
)
M240
{
1
2
1
2
}
M241
⟨
1
2
1
2
⟩
M242
⌊
1
2
1
2
⌋
M243
⌈
1
2
1
2
⌉
M244
↑
1
2
1
2
↑
M245
↓
1
2
1
2
↓
M246
↕
1
2
1
2
↕
M247
⇑
1
2
1
2
⇑
M248
⇓
1
2
1
2
⇓
M249
⇕
1
2
1
2
⇕
M250
1
2
1
2
M251
\arrowvert
1
2
1
2
\arrowvert
M252
\Arrowvert
1
2
1
2
\Arrowvert
M253
\bracevert
1
2
1
2
\bracevert
M254
|
1
2
1
2
|
M255
|
1
2
1
2
|
M256
|
1
2
1
2
|
M257
∥
1
2
1
2
∥
M258
∥
1
2
1
2
∥
M259
/
1
2
1
2
/
M260
\
1
2
1
2
\
M261
⎱
1
2
1
2
⎰
M262
\lgroup
1
2
1
2
\rgroup
M263
⌞
1
2
1
2
⌟
M264
⌜
1
2
1
2
⌝
M265
A
←
n
+
μ
−
1
B
→
T
n
±
i
−
1
C
M266
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
…
M267
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
…
M268
(
sin
⁡
θ
M
⌋
M269
(
sin
⁡
θ
M
⌋
M270
(
sin
⁡
θ
M
⌋
M271
(
sin
⁡
θ
M
⌋
M272
(
sin
⁡
θ
M
⌋
M273
(
sin
⁡
θ
M
⌋
M274
(
sin
⁡
θ
M
⌋
M275
(
sin
⁡
θ
M
⌋
M276
(
sin
⁡
θ
M
⌋
M277
sin
⁡
θ
M
M278
sin
⁡
θ
M
M279
sin
⁡
θ
M
M280
sin
⁡
θ
M
M281
sin
⁡
θ
M
M282
sin
⁡
θ
M
M283
sin
⁡
θ
M
M284
sin
⁡
θ
M
M285
sin
⁡
θ
M
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