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File: /TortureTests/Complexity/complex3.xml
Author: Mackichan (S. Swanson)
Description: around 300 equation tests
Sample Rendering: N/A

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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 ) z = n = 0 a n C z n z

M6

lim n | C [ f ( z ) k = 0 n a k z k ] 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 y + C 1 ) e 1 2 y 2

M41

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

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

( 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 2 w z 2 + z w 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 } , θ { 2 X 4 π π + ( arccos 1 7 14 ) | X 4 }

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 ) x = lim P 0 i = 1 n f ( x ¯ i ) Δ x i

M120

a b f ( x ) x = lim n b a n i = 1 n f ( a + i b a n )

M121

0 2 x 5 x 3 + 1 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 ) u

M122

f ( g ( x ) ) g ( x ) x = f ( u ) 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

f x ( x 1 ) = 5

M146

x x = x y x y = x y z x y z = x y z t x y z 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

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 )

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 ) 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

5 ( x 7 3 x 6 ) x 5    n sin x x n    3 x 3 f ( x )    2 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 ) x <

M185

( ∇× F ) k = z + 1

M186

M M M M M

M187

x x 2    x ( x 2 )    x x ( x 2 )    x 2 ( x 2 )    x y ( x 2 y 3 )    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 x = 1 not here x 2 merged y 1 jbm lowlife The end. x 2 + y 2 = z 2 1 x 2 + y 2 = z 2 1 x + y 3 = z 3 x 2 + y 2 = z 2 1 x + y 3 = z 3 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 First line of equation Middle line of equation Other middle line of equation Last line of equation L 1 = R 1    L 2 = R 2 L 3 = R 3    L 4 = R 4 ( 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 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 Vertex V ( 0 , 0 ) Focus F ( 0 , p ) Directrix y = p x    ( csc 1 x ) = 1 | x | x 2 1 tanh 1 x = 1 2 ln ( 1 + x 1 x )    1 < x < 1 α + A B C + 1 = a b c y = e P x [ e P x Q x + c ] x = 1 + y 3

and

x = 1 + y $ 1.00 + 25 ¢ 3 £ + 2.45 ¤ 0.7 ¥ a + 20 + 30 4.56 2 x + y = 3 3 x 4 y = 5 a + b = c + 12345 Unrestricted     Symmetric Antisymmetric    Triangular a b x c d y e f 11 g h Z k l 3 A B C A B C 10 11 12 x ≰⃥ y ≰⃥ z lim ¯ x lim ̲ x lim x lim x x = y + z = k + m 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 { 1 2 1 2 1 2 } 1 2 1 2 | 1 2 1 2 1 2 | 1 2 1 2 1 2 1 2 [ 1 2 1 2 ] ( 1 2 1 2 ) { 1 2 1 2 } 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 \arrowvert 1 2 1 2 \arrowvert \Arrowvert 1 2 1 2 \Arrowvert \bracevert 1 2 1 2 \bracevert | 1 2 1 2 | | 1 2 1 2 | | 1 2 1 2 | 1 2 1 2 1 2 1 2 / 1 2 1 2 / \ 1 2 1 2 \ 1 2 1 2 \lgroup 1 2 1 2 \rgroup 1 2 1 2 1 2 1 2 A n + μ 1 B T n ± i 1 C 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + ( sin θ M ( sin θ M ( sin θ M ( sin θ M ( sin θ M ( sin θ M ( sin θ M ( sin θ M ( sin θ M sin θ M sin θ M sin θ M sin θ M sin θ M sin θ M sin θ M sin θ M sin θ M

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