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File:TortureTests/Complexity/complex3
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Author:Mackichan (S. Swanson)
Description:around 300 equation tests

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2 a b x 3 f ( x ) + sin cos θ = 1 f ( z ) = n = 0 a n z n ,  | z | < R ( R 0 ) C ( n = 0 a n z n ) z = n = 0 a n C z n z lim n | C [ f ( z ) k = 0 n a k z k ] z | = 0 n N ( ε ) | f ( z ) k = 0 n a k z k | < ε 10  Bq + 10  Ci 10  amol + 10  Emol 10  fmol + 10  Gmol 10  kmol + 10  Mmol 10  μmol + 10  mmol 10  mol + 10  nmol 10  Pmol + 10  pmol 10  Tmol 10  acre + 10  hectare 10  ft 2 + 10  in 2 10  m 2 10  A + 10  kA 10  μA + 10  mA 10  nA 10  F + 10  μF 10  mF + 10  nF 10  pF 10  C + 1.0  m/s/s 0.1  m / s 2 10  kS + 10  μS 10  mS + 10  S 10  kV + 10  MV 10  μV + 10  mV 10  nV + 10  pV 10  V 10  GΩ + 10  kΩ 10  MΩ + 10  mΩ 10  Ω 10  Btu + 10  cal 10  eV + 10  erg 10  GeV + 10  GJ 10  J + 10  kcal 10  kJ + 10  MeV 10  MJ + 10  μJ 10  mJ + 10  nJ 10  dyn + 10  kN 10  MN + 10  μN 10  mN + 10  N 10  ozf + 10  lbf 10  EHz + 10  GHz 10  Hz + 10  kHz 10  MHz + 10  PHz 10  THz 10  fc + 10  lx 10  phot 10  Å + 10  am 10  cm + 10  dm 10  fm + 10  ft 10  in 10  km + 10  m 10  μm + 10  mi 10  mm + 10  nm 10  pm 10  sb 10  lm 10  cd 10  Mx + 10  μWb 10  mWb + 10  nWb 10  Wb 10  G + 10  μT 10  mT + 10  nT 10  pT + 10  T 10  H + 10  μH 10  mH 10  u + 10  cg 10  dg + 10  g 10  kg + 10  μg 10  mg + 10  lb 10  slug 10  ° + 10  μrad 10  mrad + 10 10  rad + 10 ′′ 10  GW + 10  hp 10  kW + 10  MW 10  μW + 10  mW 10  nW + 10  W 10  atm + 10  bar 10  kbar + 10  kPa 10  MPa + 10  μPa 10  mbar + 10  mmHg 10  Pa + 10  torr 10  sr 10  °C + 10  °F 10  K 10  as + 10  d 10  fs + 10  h 10  μs + 10  ms 10  min + 10  ns 10  ps + 10  s 10  y 10  ft 3 + 10  in 3 10  m 3 + 10  gal 10  l 10  ml + 10  pint 10  qt 1 x ( y ) = ( e 1 2 y 2 sin y y + C 1 ) e 1 2 y 2 x y y = sin x ( 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 ( a b ) = b a 2 5 + 3 7 = 2 7 + 3 5 35 = 29 35 | a | = { a if a 0 a if a < 0 a n = a a a n  factors ( a b ) n = ( b a ) n a n = b   means  b n = a . 16 81 4 = 16 4 81 4 = 2 3 { x x 0 , x 1 } a n x n + a n 1 x n 1 + + a 1 x + a 0 a 3 b 3 = ( a b ) ( a 2 + a b + b 2 ) ( x + y ) 2 H = { ( a b c d ) G a d b c = 1 } | x | + || y || + { z } [ a c ] + ( b ) = [ a , b ] x = 1 x = 1 x = 1 x = 1 [ 10 3 , 7 3 ) ( 7 3 , 4 3 ] A u x + B u y + C u = E x 1 < i < 10 1 < j < 10 2 i + j Γ 1 2 3 4 5 6 7 1 5 7 6 2 4 3 y ( x ) = x e x e x + 2 e x = x 1 + 2 e x x x y y = 0 y ( 0 ) = 1 y ( 0 ) = 0 y ( x ) = 1 3 e ( 1 ) 3 x + 2 3 e 1 2 ( 1 ) 3 x cos 1 2 3 ( 1 ) 3 x y ( t ) = 2 tan ( 2 t 1 4 π ) ( 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 ) x = 1 x + 3 = 123 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 K v ( z ) = BesselK v ( z ) z 2 2 w z 2 + z w z ( z 2 + v 2 ) w = 0 2 u ( x , y ) x 2 2 u ( x , y ) y 2 = 0 y ( t , x ) = F 1 ( x a t ) + F 2 ( x a t ) 1 2 3 4 5 6 2 x + 1 = 5 1 = 3 9 = 7 a b c d e f x + 2 y 3 = 5 4 x y 5 = 98 x = z 1 = 3 A 1 = N 0 ( λ ; Ω ) φ ( λ ; Ω ) , A 2 = φ ( λ ; Ω ) φ ( λ ; Ω ) , A 3 = N ( λ ; ω ) . sin θ cos γ x = { x if  x < 0 x if  x 0 L M R M L M R M M A T H M A T H ∇× F = 0 ∇· F ∇·∇ F = 2 F + 7 = A ∇× ( x y , y z , z x ) = [ y z x ] ∇× ( y , z , x ) = ( 1 , 1 , 1 ) 0 x + y + α = 102 a + b = c x + 1 x + f ( x ) 1 = 123 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 . ( 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 ) ) ( c u v + v 2 w ) = ( u v , c v , c u + 2 v w , v 2 ) 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 θ { π + 2 X 3 π ( arccos 1 7 14 ) | X 3 } , θ { 2 X 4 π π + ( arccos 1 7 14 ) | X 4 } P = A ( A T A ) 1 A T det ( x y 1 a b 1 a d 1 ) = x b x d + a d a b = 0 A ( θ ) A ( θ ) = [ cos θ sin θ sin θ cos θ ] [ cos θ sin θ sin θ cos θ ] J ( A ) = [ J n 1 ( λ 1 ) 0 0 0 J n 2 ( λ 2 ) 0 0 0 J n k ( λ k ) ] det ( 4 + X 1 0 0 4 + X 0 0 0 4 + X ) = ( X 4 ) 3 { ( 1 2 1 6 33 1 ) } 5 2 1 2 33 A = max x 0 A x x ( 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 ) f ( [ 1 2 4 3 ] ) = [ 1 2 4 3 ] 2 5 [ 1 2 4 3 ] 2 = [ 2 2 4 0 ] x = lim x = 1 1 2 a a b f ( x ) x = lim P 0 i = 1 n f ( x ¯ i ) Δ x i a b f ( x ) x = lim n b a n i = 1 n f ( a + i b a n ) 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 f ( g ( x ) ) g ( x ) x = f ( u ) u x = 2 n = 1 100 n ( n 1 ) lim x 0 sin ( 1 x ) = 1 .. 1 h ( i , j ) = ( 2 j ) g ( i ) + ( j 1 ) f ( g ( i ) ) : [ 0 , 1 ] [ 0 , 1 ] 0 x = x x y = h 1 ( h ( x ) h ( y ) ) x y = f 1 ( max { f ( x ) + f ( y ) 1 , 0 } ) x y = η ( η ( x ) η ( y ) ) x 0 y = { x y if x y = 1 0 if x y < 1 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 g ( x ) = exp ( 1 ( 1 x ) a ( 2 a 1 ) ( 1 x ) a ) Aut ( I ) = { f : [ 0 , 1 ] [ 0 , 1 ] | f  is one-to-one and onto, and x y  implies  f ( x ) f ( y ) } x 2 + y 2 = r 2 ,    tan θ = y x 2 1 t 2 [ ( 2 + sin t ) 10 cos t , ( 2 + cos t ) 10 sin t , 3 sin 3 t ] { t = 0 , s = 0 } , { t = π , s = π } 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 testing  x 2  end. x x x x f x ( x 1 ) = 5 x x = x y x y = x y z x y z = x y z t x y z t mod a 5 mod 3 = 2 f ( 0 ) mod 3 = 1 5 x + 4 8 ( mod 13 ) a = ( 5 3 ) / 5 mod 7 = 6 ( 2 x 2 + x + 2 ) + ( 2 x + 1 ) mod 3 = 2 x 2 + 0 1 000 000 111 1 1 0 4. 974 9 x F ( x ) [ 86.333 , 146.33 , 129.33 ] BinomialDist ( x ; n , p ) = k = 0 x ( n k ) p k q n k Pr ( X 54 ) = BinomialDist ( 54 ; 100 , .55 ) = .45846 k = max { | f y ( x , y ) | : ( x , y ) D } . m = lim x a f ( x ) f ( a ) x a | 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 x = 1 ( hl text  x  end. ) x = 1 ( hl to URI  x  end ) x = 1 ( sex ) x = 1 ( jbm ) f ( x ) g [ y ] h { z } + a b c 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 x x x x x x ( a 1 , a 2 , , a n ) ( b 1 , b 2 , , b n ) = a 1 b 1 * + a 2 b 2 * + + a n b n * n 5 + n 5 2 + n 5 3 + n 5 4 + x 1 + + x n x + + x k  times x 1 x 2 x n n n ! = 1 × 2 × 3 × 4 × × n P : a = x 0 < x 1 < x 2 < < x n = b f ( x ) = 30 13 cos x + 10 3 ( 100 + 9 cos 2 x 60 cos x sin ( x + 29 90 π ) ) cos ( A x ) sin ( B x ) x = cos ( B A ) x 2 ( B A ) + cos ( B + A ) x 2 ( B + A ) + C  . 235.3 + 813 = 1048. 3 max 2 x 2 ( x 3 6 x + 3 ) = 8.0 x decade = 2 century 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 ) f ( x ) = 30 13 cos x + 10 3 ( 100 + 9 cos 2 x 60 cos x sin ( x + 29 90 π ) ) R 3 ( | u 1 | 2 + | u 0 | 2 2 + | u 0 | 6 6 ) x < ( ∇× F ) k = z + 1 M M M M M 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 ) 5 24 ! x 6 x + a y 1 12.34 2 sin θ 1 0 1 1 0 ( 0 i i 0 ) [ 1 0 0 1 ] | a b c d | 1 0 1 0 11 1 2 3 4 5 testing  sin θ a ̂ + b ˇ + c ˜ + d ´ + e ` + f ˘ + g ¯ + h + i ˚ + j ˙ + k ¨ + l + m + n f ( g ( x ) ) = sin 3 x 2 + sin x 2 sin ( sin x 2 ) ( 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 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