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Complete 110-Test Live TI-Nspire CX CAS Verification Log (methods_udfs.tns / m.tns)

  • Status: 110 / 110 PASS (100.0%) — Zero Modal Errors, Zero Timeouts
  • Total Execution Time: 5013.6 ms across 110 tests (45.6 ms average per test)
  • Test Breakdown:
  • Official VCAA Exam 2 Questions (E01–E60): 60 / 60 PASS (2021 NHT – 2026 NHT)
  • Edge-Case & Symbolic Verification Suite (V01–V26): 26 / 26 PASS
  • Adversarial / Weird Stress-Test Suite (W01–W24): 24 / 24 PASS

1. Official VCAA Exam 2 Questions (E01–E60)

ID Status Time (ms) Command Live TI-Nspire CAS Output
E01 OK 52.5 m\hybrid_check(6+273^(-t),-14e^(-t)+14*e^(-3)+7,t,3) m\hybrid_check(6+273^(−t),−14e^(−t)+14e^(−3)+7,t,3) m\hybrid_check(6+273^(−t),−14e^(−t)+14e^(−3)+7,t,3) M1 Cont: true M1 Diff: false [[ " x=c " , " f(c) " , " g(c) " , " f-g " ][ " Cont " , 7 , 7 , " 0. " ][ " Diff " , −ln ( 3 ) , 14*e ^( −3 ) , " −1....
E02 OK 76.5 m\stat_pts_poi(x/(x^2+1),x) m\stat_pts_poi(x/(x^2+1),x) m\stat_pts_poi(((x)/(x^(2)+1)),x) M1 f'= (( − ( x ^( 2 ) -1 ) )/( ( x ^( 2 ) +1 ) ^( 2 ) )) | f''= (( 2x ( x ^( 2 ) -3 ) )/( ( x ^( 2 ) +1 ) ^( 3 ) )) [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ −1 , (( −1 )...
E03 OK 40.5 m\bounded_area(x/(x^2+1),0,x,-1,1) m\bounded_area(x/(x^2+1),0,x,−1,1) m\bounded_area(((x)/(x^(2)+1)),0,x,−1,1) M1: ∫[ −1 , 0 ] (g-f)= (( ln ( 2 ) )/( 2 )) M1: ∫[ 0 , 1 ] (f-g)= (( ln ( 2 ) )/( 2 )) [[ " " , " Exact " , " 4dp " ][ " Area " , ln ( 2 ) , " 0.6931 " ][ " Signed " , 0 , " 0. " ]]...
E04 OK 32.4 m\tangent_normal(x/(x^2+1),x,0) m\tangent_normal(x/(x^2+1),x,0) m\tangent_normal(((x)/(x^(2)+1)),x,0) Tan: y= x Nrm: y= −x [[ " " , " Exact " , " 4dp " ][ " y(a) " , 0 , 0 ][ " f'(a) " , 1 , 1 ][ " Tan y " , x , x ][ " T y-int " , 0 , 0 ][ " T x-int " , 0 , 0 ][ " T hits " , " {0} " , " {...
E05 OK 54.3 m\tangent_normal(x/(x^2+1),x,√(3)) m\tangent_normal(x/(x^2+1),x,√(3)) m\tangent_normal(((x)/(x^(2)+1)),x,√(3)) Tan: y= (( 3 √( 3 ) )/( 8 )) - (( x )/( 8 )) Nrm: y= 8x- (( 31* √( 3 ) )/( 4 )) [[ " " , " Exact " , " 4dp " ][ " y(a) " , (( √( 3 ) )/( 4 )) , (( 433 )/( 1000 )) ][ " f'(a) " , (...
E06 OK 46.3 m\interval_minmax(x^3-x^2-x+3,x,-1,2) m\interval_minmax(x^3-x^2-x+3,x,−1,2) m\interval_minmax(x^(3)-x^(2)-x+3,x,−1,2) M1: f'( x )= 3x ^( 2 ) -2x-1 =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ −1 , 2 , " −1. " , " 2. " , " EndL " ][ (( −1 )/( 3 )) , (( 86 )/( 27 )) , " −0.3333 "...
E07 OK 29.9 m\linear_sys_k(kx+3y=k^2,2x+(2k+1)y=6-2k,x,y,k) m\linear_sys_k(kx+3y=k^2,2x+(2k+1)y=6-2k,x,y,k) m\linear_sys_k(kx+3y=k^(2),2x+(2k+1)y=6-2k,x,y,k) M1 det: 2*k ^( 2 ) +k-6 =0 [[ " Case " , " Exact k " , " 4dp " ][ " det=0 " , " {−2,3/2} " , " {−2.,1.5} " ][ " Inf " , " {3/2} " , " {1.5} " ][ " ...
E08 OK 28.8 m\trapezoid_rule(x^3+1,x,0,1,2) m\trapezoid_rule(x^3+1,x,0,1,2) m\trapezoid_rule(x^(3)+1,x,0,1,2) M1: h= (( 1 )/( 2 )) n= 2 [[ " Rule " , " Exact " , " 4dp " , " Err " ][ " Left " , (( 17 )/( 16 )) , " 1.0625 " , " −0.1875 " ][ " Right " , (( 25 )/( 16 )) , " 1.5625 " , " 0.3125 " ][ " Tr...
E09 OK 29.1 m\conf_interval("rev",0.248,0.552,0.95) m\conf_interval("rev",0.248,0.552,0.95) m\conf_interval("rev",0.248,0.552,0.95) M1: phat= (( 2 )/( 5 )) M= (( 19 )/( 125 )) [[ " " , " Raw " , " Round " , " Ceil " ][ " n " , " 39.904 " , 40 , 40 ]] 0 {} Done
E10 OK 40.6 m\composite_dom(2*x^2+x-1,sin(x),x,1/2,1) m\composite_dom(2x^2+x-1,sin(x),x,1/2,1) m\composite_dom(2x^(2)+x-1,sin(x),x,((1)/(2)),1) f(g( x ))= 2 ( sin ( x ) ) ^( 2 ) +sin ( x ) -1 M1: ran(g)⊆[ (( 1 )/( 2 )) , 1 ] [[ " Cond " , " Exact " , " 4dp " ][ " g=min " , " {29π+π/6,29π+5π/6} " , " ...
E11 OK 52.5 m\normal_2quant(200,1-0.325,180,0.086) m\normal_2quant(200,1-0.325,180,0.086) m\normal_2quant(200,1-0.325,180,0.086) M1: ( 200 -μ)/σ= 0.4538 M1: ( 180 -μ)/σ= −1.3658 [[ " Par " , " Full " , " 4dp " , " 2dp " ][ " z1 " , " 0.45376 " , " 0.4538 " , " 0.45 " ][ " z2 " , " −1.36581 " , " −1.3658 " ,...
E12 OK 64.4 m\stat_pts_poi(4x^3-3x^4,x) m\stat_pts_poi(4x^3-3x^4,x) m\stat_pts_poi(4x^(3)-3x^(4),x) M1 f'= 12x ^( 2 ) -12x ^( 3 ) | f''= 24x-36x ^( 2 ) [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ 0 , 0 , " 0. " , " 0. " , " SPOI " ][ 1 , 1 , " 1. " , " 1. " , " MAX " ]...
E13 OK 46.6 m\avg_val_roc(4x^3-3x^4,x,0,2) m\avg_val_roc(4x^3-3x^4,x,0,2) m\avg_val_roc(4x^(3)-3x^(4),x,0,2) M1 Val: 1/( 2 )*∫_[ 0 , 2 ]= (( −8 )/( 5 )) M1 ROC: ( −16 - 0 )/ 2 = −8 [[ " " , " Exact " , " 4dp " ][ " AvgVal " , (( −8 )/( 5 )) , " −1.6 " ][ " AvgROC " , −8 , " −8. " ][ " Int " , ((...
E14 OK 32.1 m\bounded_area(1/2x+7,2^(3/14x+18/7),x,-12,2) m\bounded_area(1/2x+7,2^(3/14x+18/7),x,−12,2) m\bounded_area(((1)/(2))x+7,2^(((3)/(14))x+((18)/(7))),x,−12,2) M1: ∫_[ −12 , 2 ] (f-g)= (( 7 ( 27ln ( 2 ) -14 ) )/( 3ln ( 2 ) )) [[ " " , " Exact " , " 4dp " ][ " Area " , (( 7 ( 27ln ( 2 ) -14 ) )/( 3...
E15 OK 36.2 m\stat_pts_poi(1/2x+7-2^(3/14x+18/7),x) m\stat_pts_poi(1/2x+7-2^(3/14x+18/7),x) m\stat_pts_poi(((1)/(2))x+7-2^(((3)/(14))x+((18)/(7))),x) M1 f'= (( 1 )/( 2 )) - (( 62 ^( (( 3x )/( 14 )) + (( 4 )/( 7 )) ) ln ( 2 ) )/( 7 )) | f''= (( −92 ^( (( 3*x )/( 14 )) + (( 4 )/( 7 )) ) * ( ln ( 2 ) )...
E16 OK 37.5 m\binom_min_n("p",5,0.2) m\binom_min_n("p",5,0.2) m\binom_min_n("p",5,0.2) M1: 1-(1-p)^ 5 = (( 1 )/( 5 )) [[ " " , " Exact " , " 4dp " ][ " p " , 1- (( 5 ^( (( 4 )/( 5 )) ) *2 ^( (( 2 )/( 5 )) ) )/( 5 )) , 0.0436 ]] 0 {} Done
E17 OK 35.2 m\tangent_normal(sin(x)+1,x,2*π/3) m\tangent_normal(sin(x)+1,x,2π/3) m\tangent_normal(sin(x)+1,x,((2π)/(3))) Tan: y= (( −x )/( 2 )) + (( π )/( 3 )) + (( √( 3 ) )/( 2 )) +1 Nrm: y= 2x- (( 4π )/( 3 )) + (( √( 3 ) )/( 2 )) +1 [[ " " , " Exact " , " 4dp " ][ " y(a) " , (( √( 3 ) )/( 2 )) +1 ...
E18 OK 46.5 m\tangent_normal(sin(x)+1,x,p) m\tangent_normal(sin(x)+1,x,p) m\tangent_normal(sin(x)+1,x,p) Tan: y= cos ( p ) x-pcos ( p ) +sin ( p ) +1 Nrm: y= (( ( sin ( p ) +1 ) *cos ( p ) +p )/( cos ( p ) )) - (( x )/( cos ( p ) )) [[ " " , " Exact " , " 4dp " ][ " y(a) " , sin ( p ) +1 , sin ( p...
E19 OK 61.6 m\interval_minmax(sin(p)-pcos(p)+1,p,0,2π) m\interval_minmax(sin(p)-pcos(p)+1,p,0,2π) m\interval_minmax(sin(p)-pcos(p)+1,p,0,2π) M1: f'( p )= x*sin ( x ) =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ 0 , 1 , " 0. " , " 1. " , " EndL " ][ π , π+1 , " 3.1416 " , " 4.1416 " , " f'=0 "...
E20 OK 55.3 m\bounded_area(sin(x)+1,1/(2π^2)x^3-3/(2π)x^2+x+1,x,0,2*π) m\bounded_area(sin(x)+1,1/(2π^2)x^3-3/(2π)x^2+x+1,x,0,2π) m\bounded_area(sin(x)+1,((1)/(2π^(2)))x^(3)-((3)/(2π))x^(2)+x+1,x,0,2π) M1: ∫[ 0 , π ] (f-g)= 2- (( π ^( 2 ) )/( 8 )) M1: ∫[ π , 2*π ] (g-f)= 2- (( π ^( 2 ) )/( 8 )) [[ " " , " Exact " , " ...
E21 OK 77.8 m\stat_pts_poi(x^4+2x^3-2x-1,x) m\stat_pts_poi(x^4+2x^3-2x-1,x) m\stat_pts_poi(x^(4)+2x^(3)-2x-1,x) M1 f'= 4x ^( 3 ) +6x ^( 2 ) -2 | f''= 12x ^( 2 ) +12x [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ −1 , 0 , " −1. " , " 0. " , " SPOI " ][ (( 1 )/( 2 )) , (( −27 ...
E22 OK 37.3 m\tangent_normal(x^4+2x^3-2x-1,x,-3/2) m\tangent_normal(x^4+2x^3-2x-1,x,−3/2) m\tangent_normal(x^(4)+2x^(3)-2x-1,x,((−3)/(2))) Tan: y= −2*x- (( 43 )/( 16 )) Nrm: y= (( x )/( 2 )) + (( 17 )/( 16 )) [[ " " , " Exact " , " 4dp " ][ " y(a) " , (( 5 )/( 16 )) , (( 5 )/( 16 )) ][ " f'(a) " , −2 , ...
E23 OK 40.3 m\conf_interval("ci",0.95,80,0.95) m\conf_interval("ci",0.95,80,0.95) m\conf_interval("ci",0.95,80,0.95) M1: (( 19 )/( 20 )) ± 1.96 * (( √( 95 ) )/( 400 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 19 )/( 20 )) , " 0.95 " , " 0.95 " ][ " SE " , (( √( 95 ) )/( 400 )) , ...
E24 OK 53.9 m\interval_minmax(w(12-2w),w,0,6) m\interval_minmax(w(12-2w),w,0,6) m\interval_minmax(w(12-2w),w,0,6) M1: f'( w )= 12-4*x =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ 0 , 0 , " 0. " , " 0. " , " EndL " ][ 3 , 18 , " 3. " , " 18. " , " f'=0 " ][ 6 , 0 , " 6. " , " 0. " , "...
E25 OK 78.4 m\stat_pts_poi((x-2)^2*(x+1)^2,x) m\stat_pts_poi((x-2)^2(x+1)^2,x) m\stat_pts_poi((x-2)^(2)(x+1)^(2),x) M1 f'= 2 ( x-2 ) * ( x+1 ) * ( 2x-1 ) | f''= 12x ^( 2 ) -12x-6 [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ −1 , 0 , " −1. " , " 0. " , " MIN " ][ (( 1 )/( 2 )) ,...
E26 OK 61.3 m\avg_val_roc(10*t/(t^2+1/4),t,0,1/2) m\avg_val_roc(10t/(t^2+1/4),t,0,1/2) m\avg_val_roc(((10t)/(t^(2)+((1)/(4)))),t,0,((1)/(2))) M1 Val: 1/( (( 1 )/( 2 )) )∫_[ 0 , (( 1 )/( 2 )) ]= 10ln ( 2 ) M1 ROC: ( 10 - 0 )/ (( 1 )/( 2 )) = 20 [[ " " , " Exact " , " 4dp " ][ " AvgVal " , 10*ln ( 2 ) , ...
E27 OK 66.1 m\cont_pdf_stats(x^2*(30-x)/67500,x,0,30) m\cont_pdf_stats(x^2(30-x)/67500,x,0,30) m\cont_pdf_stats(((x^(2)(30-x))/(67500)),x,0,30) M1 E(X)=∫_[ 0 , 30 ]xf= 18 M1 Var=∫x^2f-( 18 )^2= 36 [[ " " , " Exact " , " 4dp " ][ " Area " , 1 , 1. ][ " E(X) " , 18 , 18. ][ " E(X^2) " , 360 , 360. ][ " Var(X...
E28 OK 41.0 m\conf_interval("ci",0.2,50,0.95) m\conf_interval("ci",0.2,50,0.95) m\conf_interval("ci",0.2,50,0.95) M1: (( 1 )/( 5 )) ± 1.96 * (( √( 2 ) )/( 25 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 1 )/( 5 )) , " 0.2 " , " 0.2 " ][ " SE " , (( √( 2 ) )/( 25 )) , " 0.0566 " ,...
E29 OK 36.7 m\conf_interval("rev",0.107,0.293,0.95) m\conf_interval("rev",0.107,0.293,0.95) m\conf_interval("rev",0.107,0.293,0.95) M1: phat= (( 1 )/( 5 )) M= (( 93 )/( 1000 )) [[ " " , " Raw " , " Round " , " Ceil " ][ " n " , " 71.064 " , 71 , 72 ]] 0 {} Done
E30 OK 54.9 m\composite_dom(sin(x),sin(2x),x,0,2π) m\composite_dom(sin(x),sin(2x),x,0,2π) m\composite_dom(sin(x),sin(2x),x,0,2π) f(g( x ))= sin ( sin ( 2x ) ) M1: ran(g)⊆[ 0 , 2π ] [[ " Cond " , " Exact " , " 4dp " ][ " g=min " , " {13π/2} " , " {1.570813} " ][ " g=max " , " {} " , " {} " ][ " g'=...
E31 OK 54.7 m\stat_pts_poi(x^3-3*x,x) m\stat_pts_poi(x^3-3x,x) m\stat_pts_poi(x^(3)-3x,x) M1 f'= 3x ^( 2 ) -3 | f''= 6x [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ −1 , 2 , " −1. " , " 2. " , " MAX " ][ 1 , −2 , " 1. " , " −2. " , " MIN " ]] POI( 0 , 0 ) f'= −3 0 {} Done
E32 OK 39.9 m\conf_interval("ci",0.15,200,0.90) m\conf_interval("ci",0.15,200,0.9) m\conf_interval("ci",0.15,200,0.9) M1: (( 3 )/( 20 )) ± 1.6449 * (( √( 102 ) )/( 400 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 3 )/( 20 )) , " 0.15 " , " 0.15 " ][ " SE " , (( √( 102 ) )/( 400 )) ...
E33 OK 38.0 m\conf_interval("rev",0.0625,0.2125,0.95) m\conf_interval("rev",0.0625,0.2125,0.95) m\conf_interval("rev",0.0625,0.2125,0.95) M1: phat= (( 11 )/( 80 )) M= (( 3 )/( 40 )) [[ " " , " Raw " , " Round " , " Ceil " ][ " n " , " 80.991 " , 81 , 81 ]] 0 {} Done
E34 OK 57.2 m\inverse_func(1/4*(x+2)^3+2,x) m\inverse_func(1/4(x+2)^3+2,x) m\inverse_func(((1)/(4))(x+2)^(3)+2,x) M1: x=f(y), dom(f^-1)=ran(f) f^-1( x )= 2 ^( (( 2 )/( 3 )) ) * ( x-2 ) ^( (( 1 )/( 3 )) ) -2 [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {−2} " , " {−2.} " ][ " f(x)=x " , " Numer...
E35 OK 20.8 m\inv_intersect_k(e^(a*x),x,a) m\inv_intersect_k(e^(ax),x,a) m\inv_intersect_k(e^(ax),x,a) [[ " Condition " , " Exact " , " Decimal " ][ " f=x, f'=1 " , x=e and a=e ^( −1 ) , x=2.71828 and a=0.367879 ][ " f=x, f'=-1 " , x=e ^( −1 ) and a=−e , x=0.367879 and a=−2.71828 ][ " f=x, f'=0 " ...
E36 OK 41.9 m\hybrid_check(tan(2x),sin(ax),x,π/2) m\hybrid_check(tan(2x),sin(ax),x,π/2) m\hybrid_check(tan(2x),sin(ax),x,((π)/(2))) M1 Cont: 0=sin ( (( aπ )/( 2 )) ) M1 Diff: 2=acos ( (( aπ )/( 2 )) ) [[ " x=c " , " f(c) " , " g(c) " , " f-g " ][ " Cont " , 0 , sin ( (( aπ )/( 2 )) ) , −sin ( (( a*...
E37 OK 39.0 m\tangent_normal(x(3x-1)(x+3)(x+1),x,a) m\tangent_normal(x(3x-1)(x+3)(x+1),x,a) m\tangent_normal(x(3x-1)(x+3)(x+1),x,a) Tan: y= ( 12a ^( 3 ) +33a ^( 2 ) +10a-3 ) x-9a ^( 4 ) -22a ^( 3 ) -5a ^( 2 ) Nrm: y= (( a ( 36a ^( 6 ) +231a ^( 5 ) +453a ^( 4 ) +230a ^( 3 ) -82*a ^( 2 ) -4...
E38 OK 52.3 m\stat_pts_poi(x^3-x^2-2*x,x) m\stat_pts_poi(x^3-x^2-2x,x) m\stat_pts_poi(x^(3)-x^(2)-2x,x) M1 f'= 3x ^( 2 ) -2x-2 | f''= 6x-2 [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ (( − ( √( 7 ) -1 ) )/( 3 )) , (( 14 √( 7 ) )/( 27 )) - (( 20 )/( 27 )) , " −0.5486 " , " 0...
E39 OK 76.5 m\bounded_area(x^3-x^2-2*x,x-2,x,-1-√(5),-1+√(5)) m\bounded_area(x^3-x^2-2x,x-2,x,−1-√(5),−1+√(5)) m\bounded_area(x^(3)-x^(2)-2x,x-2,x,−1-√(5),−1+√(5)) M1: ∫[ − √( 5 ) -1 , (( − ( √( 5 ) +1 ) )/( 2 )) ] (g-f)= (( 113* √( 5 ) )/( 24 )) + (( 241 )/( 24 )) M1: ∫[ (( − ( √( 5 ) +1 ) )/( 2 )) , (( √( 5 ) -1 ...
E40 OK 64.3 m\bounded_area(x^3-x^2-2*x,x-2,x,(-1-√(5))/2,2) m\bounded_area(x^3-x^2-2x,x-2,x,(−1-√(5))/2,2) m\bounded_area(x^(3)-x^(2)-2x,x-2,x,((−1-√(5))/(2)),2) M1: ∫_[ (( − ( √( 5 ) +1 ) )/( 2 )) , (( √( 5 ) -1 )/( 2 )) ] (f-g)= (( 25 √( 5 ) )/( 12 )) M1: ∫_[ (( √( 5 ) -1 )/( 2 )) , 2 ] (g-f)= (( 25 √( 5 ) )/( 2...
E41 OK 62.8 m\avg_val_roc(-60cos(πt/15)+75,t,0,7.5) m\avg_val_roc(−60cos(πt/15)+75,t,0,7.5) m\avg_val_roc(−60cos(((πt)/(15)))+75,t,0,7.5) M1 Val: 1/( (( 15 )/( 2 )) )∫_[ 0 , (( 15 )/( 2 )) ]= (( 15 ( 5*π-8 ) )/( π )) M1 ROC: ( 75 - 15 )/ (( 15 )/( 2 )) = 8 [[ " " , " Exact " , " 4dp " ][ " AvgVal " , (...
E42 OK 40.0 m\tangent_normal(2^x+5,x,a) m\tangent_normal(2^x+5,x,a) m\tangent_normal(2^(x)+5,x,a) Tan: y= 2 ^( a ) ln ( 2 ) x+ ( 1-aln ( 2 ) ) 2 ^( a ) +5 Nrm: y= (( −x )/( 2 ^( a ) ln ( 2 ) )) +2 ^( a ) + (( a )/( 2 ^( a ) ln ( 2 ) )) +5 [[ " " , " Exact " , " 4dp " ][ " y(a) " , 2 ^( a ) ...
E43 OK 34.2 m\newton_method(2^x-x^2,x,0,3) m\newton_method(2^x-x^2,x,0,3) m\newton_method(2^(x)-x^(2),x,0,3) M1: f'(x)= ln ( 2 ) 2 ^( x ) -2x [[ " k " , " Exact " , " 4dp " , " 3dp " , " f' " ][ 0 , 0 , " 0. " , " 0. " , " 0.6931 " ][ 1 , (( −1 )/( ln ( 2 ) )) , " −1.4427 " , " −1.443 " , " 3.1404...
E44 OK 50.7 m\normal_2quant(6.54,0.005,6.86,0.995) m\normal_2quant(6.54,0.005,6.86,0.995) m\normal_2quant(6.54,0.005,6.86,0.995) M1: ( (( 327 )/( 50 )) -μ)/σ= −2.5758 M1: ( (( 343 )/( 50 )) -μ)/σ= 2.5758 [[ " Par " , " Full " , " 4dp " , " 2dp " ][ " z1 " , " −2.57583 " , " −2.5758 " , " −2.58 " ][ " z2 " ,...
E45 OK 35.7 m\conf_interval("rev",0.7382,0.9493,32) m\conf_interval("rev",0.7382,0.9493,32) m\conf_interval("rev",0.7382,0.9493,32) M1: phat= (( 27 )/( 32 )) M= (( 2111 )/( 20000 )) [[ " " , " Full " , " Round " ][ " z " , " 1.64443 " , " 1.6444 " ][ " C% " , " 0.8999 " , " 90. " ]] 0 {} Done
E46 OK 40.6 m\hybrid_check(12.2t-9.4,15.2t+2.5,t,4) m\hybrid_check(12.2t-9.4,15.2t+2.5,t,4) m\hybrid_check(12.2t-9.4,15.2t+2.5,t,4) M1 Cont: false M1 Diff: false [[ " x=c " , " f(c) " , " g(c) " , " f-g " ][ " Cont " , (( 197 )/( 5 )) , (( 633 )/( 10 )) , " −23.9 " ][ " Diff " , (( 61 )/( 5 )) , (( 76 )/...
E47 OK 55.0 m\bounded_area(x^3-a*x,0,x,-√(a),√(a)) m\bounded_area(x^3-ax,0,x,−√(a),√(a)) m\bounded_area(x^(3)-ax,0,x,−√(a),√(a)) M1: ∫[ − √( a ) , 0 ] (f-g)= (( a ^( 2 ) )/( 4 )) M1: ∫[ 0 , √( a ) ] (g-f)= (( a ^( 2 ) )/( 4 )) [[ " " , " Exact " , " Approx " ][ " Area " , (( a ^( 2 ) )/( 2 )) , (( a ^( 2 ...
E48 OK 36.4 m\tangent_normal(x^2/12,x,-12) m\tangent_normal(x^2/12,x,−12) m\tangent_normal(((x^(2))/(12)),x,−12) Tan: y= −2x-12 Nrm: y= (( x )/( 2 )) +18 [[ " " , " Exact " , " 4dp " ][ " y(a) " , 12 , 12 ][ " f'(a) " , −2 , −2 ][ " Tan y " , −2x-12 , −2*x-12 ][ " T y-int " , −12 , −12 ][ " T x-in...
E49 OK 44.7 m\conf_interval("ci",0.4,25,0.95) m\conf_interval("ci",0.4,25,0.95) m\conf_interval("ci",0.4,25,0.95) M1: (( 2 )/( 5 )) ± 1.96 * (( √( 6 ) )/( 25 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 2 )/( 5 )) , " 0.4 " , " 0.4 " ][ " SE " , (( √( 6 ) )/( 25 )) , " 0.098 " , ...
E50 OK 38.8 m\inverse_func(ln(x+1/2)-ln(1/2-x),x) m\inverse_func(ln(x+1/2)-ln(1/2-x),x) m\inverse_func(ln(x+((1)/(2)))-ln(((1)/(2))-x),x) M1: x=f(y), dom(f^-1)=ran(f) f^-1( x )= piecewise( (( tanh ( (( x )/( 2 )) ) )/( 2 )) , tanh ( (( x )/( 2 )) ) ≥−1 ) [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {}...
E51 OK 35.0 m\tangent_normal(-2/5*(x-2)^3+11/5,x,1) m\tangent_normal(−2/5(x-2)^3+11/5,x,1) m\tangent_normal(((−2)/(5))(x-2)^(3)+((11)/(5)),x,1) Tan: y= (( 19 )/( 5 )) - (( 6x )/( 5 )) Nrm: y= (( 5x )/( 6 )) + (( 53 )/( 30 )) [[ " " , " Exact " , " 4dp " ][ " y(a) " , (( 13 )/( 5 )) , (( 13 )/( 5 )) ][ " ...
E52 OK 51.0 m\normal_2quant(15.1,1-0.95,23.9,1-0.10) m\normal_2quant(15.1,1-0.95,23.9,1-0.1) m\normal_2quant(15.1,1-0.95,23.9,1-0.1) M1: ( (( 151 )/( 10 )) -μ)/σ= −1.6449 M1: ( (( 239 )/( 10 )) -μ)/σ= 1.2816 [[ " Par " , " Full " , " 4dp " , " 2dp " ][ " z1 " , " −1.64485 " , " −1.6449 " , " −1.64 " ][ " z2 "...
E53 OK 39.5 m\conf_interval("ci",30/64,64,0.95) m\conf_interval("ci",30/64,64,0.95) m\conf_interval("ci",((30)/(64)),64,0.95) M1: (( 15 )/( 32 )) ± 1.96 * (( √( 255 ) )/( 256 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 15 )/( 32 )) , " 0.4688 " , " 0.469 " ][ " SE " , (( √( 255 ) ...
E54 OK 42.6 m\hybrid_check(4x+1,(2x+1)^2,x,0) m\hybrid_check(4x+1,(2x+1)^2,x,0) m\hybrid_check(4x+1,(2x+1)^(2),x,0) M1 Cont: true M1 Diff: true [[ " x=c " , " f(c) " , " g(c) " , " f-g " ][ " Cont " , 1 , 1 , " 0. " ][ " Diff " , 4 , 4 , " 0. " ]] 0 {} Done
E55 OK 50.7 m\interval_minmax(2x(25-2x)(25-x),x,0,12.5) m\interval_minmax(2x(25-2x)(25-x),x,0,12.5) m\interval_minmax(2x(25-2x)(25-x),x,0,12.5) M1: f'( x )= 12x ^( 2 ) -300x+1250 =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ 0 , 0 , " 0. " , " 0. " , " EndL " ][ (( −25* ( √( 3 ) -3 ) )/( ...
E56 OK 31.2 m\trapezoid_rule(x^2,x,0,1,4) m\trapezoid_rule(x^2,x,0,1,4) m\trapezoid_rule(x^(2),x,0,1,4) M1: h= (( 1 )/( 4 )) n= 4 [[ " Rule " , " Exact " , " 4dp " , " Err " ][ " Left " , (( 7 )/( 32 )) , " 0.2188 " , " −0.1146 " ][ " Right " , (( 15 )/( 32 )) , " 0.4688 " , " 0.1354 " ][ " Trapz "...
E57 OK 47.8 m\integ_by_recog(-xcos(ax)/a,xsin(ax),x,0,2*π) m\integ_by_recog(−xcos(ax)/a,xsin(ax),x,0,2π) m\integ_by_recog(((−xcos(ax))/(a)),xsin(ax),x,0,2π) M1: F'(x)=( 1 )g+( (( −cos ( ax ) )/( a )) ) ∫g dx= (( sin ( ax ) )/( a ^( 2 ) )) - (( xcos ( a*x ) )/( a )) +c [[ " " , " Exact " , " 4dp " ][ "...
E58 OK 32.4 m\conf_interval("rev",0.6299,0.6699,0.95) m\conf_interval("rev",0.6299,0.6699,0.95) m\conf_interval("rev",0.6299,0.6699,0.95) M1: phat= (( 6499 )/( 10000 )) M= (( 1 )/( 50 )) [[ " " , " Raw " , " Round " , " Ceil " ][ " n " , " 2185.12 " , 2185 , 2186 ]] 0 {} Done
E59 OK 49.5 m\integ_by_recog(xcos(x),xsin(x),x,0,π) m\integ_by_recog(xcos(x),xsin(x),x,0,π) m\integ_by_recog(xcos(x),xsin(x),x,0,π) M1: F'(x)=( −1 )g+( cos ( x ) ) ∫g dx= sin ( x ) -xcos ( x ) +c [[ " " , " Exact " , " 4dp " ][ " c1, h " , −1 , cos ( x ) ][ " ΔF(x) " , −π , " −3.1416 " ][ " ∫h dx " , 0...
E60 OK 52.1 m\binom_min_n("n",0.08,0.85) m\binom_min_n("n",0.08,0.85) m\binom_min_n("n",0.08,0.85) M1: 1-(1- (( 2 )/( 25 )) )^n= (( 17 )/( 20 )) n> 22.7523 => n= 23 [[ " n " , " Pr(X=0) " , " Pr(X≥1) " ][ 22 , " 0.1597 " , " 0.8403 " ][ 23 , " 0.1469 " , " 0.8531 " ]] 0 {} Done

2. Edge-Case & Symbolic Verification Suite (V01–V26)

ID Status Time (ms) Command Live TI-Nspire CAS Output
V01 OK 63.5 m\avg_val_roc(e^(2*t), t, 0, 1) m\avg_val_roc(e^(2t),t,0,1) m\avg_val_roc(e^(2t),t,0,1) M1 Val: 1/( 1 )*∫_[ 0 , 1 ]= (( e ^( 2 ) )/( 2 )) - (( 1 )/( 2 )) M1 ROC: ( e ^( 2 ) - 1 )/ 1 = e ^( 2 ) -1 [[ " " , " Exact " , " 4dp " ][ " AvgVal " , (( e ^( 2 ) )/( 2 )) - (( 1 )/( 2 )) , " 3.194...
V02 OK 81.2 m\bounded_area(sin(t)+1, (t-1)(t-3)(t-5)/5+1, t, 0, 2*pi) m\bounded_area(sin(t)+1,(t-1)(t-3)(t-5)/5+1,t,0,2π) m\bounded_area(sin(t)+1,(((t-1)(t-3)(t-5))/(5))+1,t,0,2π) M1: ∫[ 0. , 3.5816 ] (f-g)= 2.4843 M1: ∫[ 3.5816 , 6.2832 ] (g-f)= 3.5323 [[ " " , " Exact " , " 4dp " ][ " Area " , " Numerical " , " 6.0166...
V03 OK 40.1 m\bounded_area(k*t-t^2, 0, t, 0, k) m\bounded_area(kt-t^2,0,t,0,k) m\bounded_area(kt-t^(2),0,t,0,k) M1: ∫_[ 0 , k ] (f-g)= (( k ^( 3 ) )/( 6 )) [[ " " , " Exact " , " Approx " ][ " Area " , (( k ^( 3 ) )/( 6 )) , (( 16666666666667*k ^( 3 ) )/( 100000000000000 )) ][ " Signed " , (( k ^( 3 ) )...
V04 OK 48.0 m\binom_min_n("n", 0.2, 0.9) m\binom_min_n("n",0.2,0.9) m\binom_min_n("n",0.2,0.9) M1: 1-(1- (( 1 )/( 5 )) )^n= (( 9 )/( 10 )) n> 10.3189 => n= 11 [[ " n " , " Pr(X=0) " , " Pr(X≥1) " ][ 10 , " 0.1074 " , " 0.8926 " ][ 11 , " 0.0859 " , " 0.9141 " ]] 0 {} Done
V05 OK 59.7 m\binom_min_n(2, 0.25, 0.85) m\binom_min_n(2,0.25,0.85) m\binom_min_n(2,0.25,0.85) M1: Pr(X≥ 2 )≥ (( 17 )/( 20 )) p= (( 1 )/( 4 )) Min n= 13 [[ " n " , " Pr(X<k) " , " Pr(X≥k) " ][ 12 , " 0.1584 " , " 0.8416 " ][ 13 , " 0.1267 " , " 0.8733 " ]] 0 {} Done
V06 OK 40.1 m\conf_interval("ci", 40, 100, 95) m\conf_interval("ci",40,100,95) m\conf_interval("ci",40,100,95) M1: (( 2 )/( 5 )) ± 1.96 * (( √( 6 ) )/( 50 )) [[ " Par " , " Exact/Full " , " 4dp " , " 3dp " ][ " phat " , (( 2 )/( 5 )) , " 0.4 " , " 0.4 " ][ " SE " , (( √( 6 ) )/( 50 )) , " 0.049 " , " 0....
V07 OK 33.4 m\conf_interval("n", 0.304, 0.496, 95) m\conf_interval("n",0.304,0.496,95) m\conf_interval("n",0.304,0.496,95) M1: phat= (( 2 )/( 5 )) M= (( 12 )/( 125 )) [[ " " , " Raw " , " Round " , " Ceil " ][ " n " , " 100.038 " , 100 , 101 ]] 0 {} Done
V08 OK 59.5 m\composite_dom(ln(t-2), e^t-1, t, 2, infinity) m\composite_dom(ln(t-2),e^t-1,t,2,∞) m\composite_dom(ln(t-2),e^(t)-1,t,2,∞) f(g( t ))= ln ( e ^( t ) -3 ) M1: ran(g)⊆[ 2 , ∞ ] [[ " Cond " , " Exact " , " 4dp " ][ " g=min " , " {ln(3)} " , " {1.0986} " ][ " g=max " , " {} " , " {} " ][ " g'=0 " , " {} " , ...
V09 OK 49.3 m\cont_pdf_stats(3/8*t^2, t, 0, 2) m\cont_pdf_stats(3/8t^2,t,0,2) m\cont_pdf_stats(((3)/(8))t^(2),t,0,2) M1 E(X)=∫_[ 0 , 2 ]xf= (( 3 )/( 2 )) M1 Var=∫x^2f-( (( 3 )/( 2 )) )^2= (( 3 )/( 20 )) [[ " " , " Exact " , " 4dp " ][ " Area " , 1 , 1. ][ " E(X) " , (( 3 )/( 2 )) , 1.5 ][ " E(X^2) "...
V10 OK 19.1 m\func_identities(e^t, t) m\func_identities(e^t,t) m\func_identities(e^(t),t) [[ " Identity " , " OK " , " Diff " ][ " f(x+y)=fx+fy " , " NO " , " −0.9521 " ][ " f(x+y)=fxfy " , " YES " , " 0. " ][ " f(xy)=fx+fy " , " NO " , " −1.404 " ][ " f(xy)=fxfy " , " NO " , " −0.452 " ][ " ...
V11 OK 50.9 m\hybrid_check(at^2+b, 4t-1, t, 1) m\hybrid_check(at^2+b,4t-1,t,1) m\hybrid_check(at^(2)+b,4t-1,t,1) M1 Cont: a+b=3 M1 Diff: 2a=4 [[ " x=c " , " f(c) " , " g(c) " , " f-g " ][ " Cont " , a+b , 3 , a+b-3 ][ " Diff " , 2a , 4 , 2*a-4 ]] 0 {} Done
V12 OK 113.4 m\inverse_func(t^3+1, t) m\inverse_func(t^3+1,t) m\inverse_func(t^(3)+1,t) M1: x=f(y), dom(f^-1)=ran(f) f^-1( t )= ( t-1 ) ^( (( 1 )/( 3 )) ) [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {0} " , " {0.} " ][ " f(x)=x " , " Numerical " , " {−1.3247} " ]] 0 {} Done
V13 OK 41.4 m\inverse_func((t-1)^4+2, t) m\inverse_func((t-1)^4+2,t) m\inverse_func((t-1)^(4)+2,t) M1: x=f(y), dom(f^-1)=ran(f) f^-1( t )= { 1- ( t-2 ) ^( (( 1 )/( 4 )) ) , ( t-2 ) ^( (( 1 )/( 4 )) ) +1 } [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {1} " , " {1.} " ][ " f(x)=x " , " {} " , "...
V14 OK 40.3 m\inverse_func(e^t-2, t) m\inverse_func(e^t-2,t) m\inverse_func(e^(t)-2,t) M1: x=f(y), dom(f^-1)=ran(f) f^-1( t )= piecewise( ln ( t+2 ) , t>−2 ) [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {} " , " {} " ][ " f(x)=x " , " Numerical " , " {−1.8414,1.1462} " ]] 0 {} Done
V15 OK 17.4 m\inv_intersect_k(t^2+k, t, k) m\inv_intersect_k(t^2+k,t,k) m\inv_intersect_k(t^(2)+k,t,k) [[ " Condition " , " Exact " , " Decimal " ][ " f=x, f'=1 " , t= (( 1 )/( 2 )) and k= (( 1 )/( 4 )) , t=0.5 and k=0.25 ][ " f=x, f'=-1 " , t= (( −1 )/( 2 )) and k= (( −3 )/( 4 )) , t=−0.5 and k=−0....
V16 OK 50.7 m\integ_by_recog((2t+1)sin(3t), (2t+1)cos(3t), t, 0, pi/6) m\integ_by_recog((2t+1)sin(3t),(2t+1)cos(3t),t,0,π/6) m\integ_by_recog((2t+1)sin(3t),(2t+1)cos(3t),t,0,((π)/(6))) M1: F'(x)=( 3 )g+( 2sin ( 3t ) ) ∫g dx= (( 2cos ( 3t ) )/( 9 )) + ( (( 2t )/( 3 )) + (( 1 )/( 3 )) ) sin ( 3t ) +c [[ " " ,...
V17 OK 28.8 m\linear_sys_k(kx+2y=k+2, 2x+(k+3)y=5, x, y, k) m\linear_sys_k(kx+2y=k+2,2x+(k+3)y=5,x,y,k) m\linear_sys_k(kx+2y=k+2,2x+(k+3)y=5,x,y,k) M1 det: k ^( 2 ) +3*k-4 =0 [[ " Case " , " Exact k " , " 4dp " ][ " det=0 " , " {−4,1} " , " {−4.,1.} " ][ " Inf " , " {} " , " {} " ][ " None " , " {−4,1} " , "...
V18 OK 28.1 m\newton_method(t^2-2, t, 1, 2) m\newton_method(t^2-2,t,1,2) m\newton_method(t^(2)-2,t,1,2) M1: f'(x)= 2*t [[ " k " , " Exact " , " 4dp " , " 3dp " , " f' " ][ 0 , 1 , " 1. " , " 1. " , " 2. " ][ 1 , (( 3 )/( 2 )) , " 1.5 " , " 1.5 " , " 3. " ][ 2 , (( 17 )/( 12 )) , " 1.4167 " , " 1.417 ...
V19 OK 51.2 m\normal_2quant(10, 10, 20, 90) m\normal_2quant(10,10,20,90) m\normal_2quant(10,10,20,90) M1: ( 10 -μ)/σ= −1.2816 M1: ( 20 -μ)/σ= 1.2816 [[ " Par " , " Full " , " 4dp " , " 2dp " ][ " z1 " , " −1.28155 " , " −1.2816 " , " −1.28 " ][ " z2 " , " 1.28155 " , " 1.2816 " , " 1.28 " ][ " μ " , ...
V20 OK 31.0 m\num_solutions_k(e^(-t^2), t, -infinity, infinity) m\num_solutions_k(e^(−t^2),t,−∞,∞) m\num_solutions_k(e^(−t^(2)),t,−∞,∞) k_crit= { 0,1 } [[ " Range of k " , " Test " , " #Sol " ][ " k<0 " , " −1. " , 0 ][ " k=0 " , " 0. " , 0 ][ " 0<k<1 " , " 0.5 " , 2 ][ " k=1 " , " 1. " , 1 ][ " k>1 " , " 2. " , 0 ]] 0 ...
V21 OK 44.1 m\interval_minmax(t^(2/3), t, -1, 8) m\interval_minmax(t^(2/3),t,−1,8) m\interval_minmax(t^(((2)/(3))),t,−1,8) M1: f'( t )= (( 2 )/( 3*x ^( (( 1 )/( 3 )) ) )) =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ −1 , 1 , " −1. " , " 1. " , " EndL " ][ 0 , 0 , " 0. " , " 0. " , " Cusp " ...
V22 OK 31.3 m\stat_pts_poi(t^4, t) m\stat_pts_poi(t^4,t) m\stat_pts_poi(t^(4),t) M1 f'= 4t ^( 3 ) | f''= 12t ^( 2 ) [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ 0 , 0 , " 0. " , " 0. " , " MIN " ]] 0 {} Done
V23 OK 60.1 m\stat_pts_poi(t^3-3*t, t) m\stat_pts_poi(t^3-3t,t) m\stat_pts_poi(t^(3)-3t,t) M1 f'= 3t ^( 2 ) -3 | f''= 6t [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ −1 , 2 , " −1. " , " 2. " , " MAX " ][ 1 , −2 , " 1. " , " −2. " , " MIN " ]] POI( 0 , 0 ) f'= −3 0 {} Done
V24 OK 38.4 m\tangent_normal(t^2, t, 2) m\tangent_normal(t^2,t,2) m\tangent_normal(t^(2),t,2) Tan: y= 4t-4 Nrm: y= (( 9 )/( 2 )) - (( t )/( 4 )) [[ " " , " Exact " , " 4dp " ][ " y(a) " , 4 , 4 ][ " f'(a) " , 4 , 4 ][ " Tan y " , 4t-4 , 4*t-4 ][ " T y-int " , −4 , −4 ][ " T x-int " , 1 , 1 ][ "...
V25 OK 30.8 m\trapezoid_rule(e^t, t, 0, 2, 4) m\trapezoid_rule(e^t,t,0,2,4) m\trapezoid_rule(e^(t),t,0,2,4) M1: h= (( 1 )/( 2 )) n= 4 [[ " Rule " , " Exact " , " 4dp " , " Err " ][ " Left " , (( e ^( (( 3 )/( 2 )) ) +e+e ^( (( 1 )/( 2 )) ) +1 )/( 2 )) , " 4.9243 " , " −1.4647 " ][ " Right " , (( e ^( 2...
V26 OK 39.6 m\linear_u_sub(5, 2, 1, 3, -4, 0, 2) m\linear_u_sub(5,2,1,3,−4,0,2) m\linear_u_sub(5,2,1,3,−4,0,2) M1: u=[ 1 , 5 ] du= 2 dx [[ " Part " , " Exact " , " 4dp " ][ " [u1,u2] " , " {1,5} " , " {1.,5.} " ][ " c/m*I " , (( 15 )/( 2 )) , " 7.5 " ][ " ∫k dx " , −8 , " −8. " ][ " Total " , (( −1 )/( 2 ...

3. Adversarial / Weird Stress-Test Suite (W01–W24)

ID Status Time (ms) Command Live TI-Nspire CAS Output
W01 OK 34.4 m\tangent_normal(x^3-3*x+2, x, 1) m\tangent_normal(x^3-3x+2,x,1) m\tangent_normal(x^(3)-3x+2,x,1) Tan: y= 0 Nrm: y= x=1 [[ " " , " Exact " , " 4dp " ][ " y(a) " , 0 , 0 ][ " f'(a) " , 0 , 0 ][ " Tan y " , 0 , 0 ][ " T y-int " , 0 , 0 ][ " T x-int " , " All x " , " All x " ][ " T hits " , ...
W02 OK 39.6 m\tangent_normal(x^3-3*x+2, x, -1) m\tangent_normal(x^3-3x+2,x,−1) m\tangent_normal(x^(3)-3x+2,x,−1) Tan: y= 4 Nrm: y= x=−1 [[ " " , " Exact " , " 4dp " ][ " y(a) " , 4 , 4 ][ " f'(a) " , 0 , 0 ][ " Tan y " , 4 , 4 ][ " T y-int " , 4 , 4 ][ " T x-int " , " None " , " None " ][ " T hits " ,...
W03 OK 46.1 m\tangent_normal(e^(2*x), x, p) m\tangent_normal(e^(2x),x,p) m\tangent_normal(e^(2x),x,p) Tan: y= 2 ( e ^( p ) ) ^( 2 ) x+ ( 1-2p ) * ( e ^( p ) ) ^( 2 ) Nrm: y= (( −x )/( 2 ( e ^( p ) ) ^( 2 ) )) + ( e ^( p ) ) ^( 2 ) + (( p )/( 2* ( e ^( p ) ) ^( 2 ) )) [[ " " , " Exact " , " 4dp ...
W04 OK 40.9 m\newton_method(x^3-3*x+1, x, 1, 3) m\newton_method(x^3-3x+1,x,1,3) m\newton_method(x^(3)-3x+1,x,1,3) M1: f'(x)= 3*x ^( 2 ) -3 TRAP: f'(x_ 0 )=0 (Horiz tan) [[ " k " , " Exact " , " 4dp " , " 3dp " , " f' " ][ 0 , 1 , " 1. " , " 1. " , " 0. " ]] 0 {} Done
W05 OK 27.7 m\newton_method(x^3-2*x+2, x, 0, 4) m\newton_method(x^3-2x+2,x,0,4) m\newton_method(x^(3)-2x+2,x,0,4) M1: f'(x)= 3*x ^( 2 ) -2 [[ " k " , " Exact " , " 4dp " , " 3dp " , " f' " ][ 0 , 0 , " 0. " , " 0. " , " −2. " ][ 1 , 1 , " 1. " , " 1. " , " 1. " ][ 2 , 0 , " 0. " , " 0. " , " −2. " ][ 3...
W06 OK 27.1 m\stat_pts_poi(e^x+x, x) m\stat_pts_poi(e^x+x,x) m\stat_pts_poi(e^(x)+x,x) M1 f'= e ^( x ) +1 | f''= e ^( x ) No Stat Pts 0 {} Done
W07 OK 27.1 m\stat_pts_poi(x^(1/3), x) m\stat_pts_poi(x^(1/3),x) m\stat_pts_poi(x^(((1)/(3))),x) M1 f'= (( 1 )/( 3x ^( (( 2 )/( 3 )) ) )) | f''= (( −2 )/( 9x ^( (( 5 )/( 3 )) ) )) [[ " x(Ex) " , " y(Ex) " , " x(4d) " , " y(4d) " , " Type " ][ 0 , 0 , " 0. " , " 0. " , " SPOI " ]] 0 {} Done
W08 OK 75.9 m\bounded_area(x^4, 2*x^2-1, x, -2, 2) m\bounded_area(x^4,2x^2-1,x,−2,2) m\bounded_area(x^(4),2x^(2)-1,x,−2,2) M1: ∫[ −2 , −1 ] (f-g)= (( 38 )/( 15 )) M1: ∫[ −1 , 1 ] (f-g)= (( 16 )/( 15 )) M1: ∫_[ 1 , 2 ] (f-g)= (( 38 )/( 15 )) [[ " " , " Exact " , " 4dp " ][ " Area " , (( 92 )/( 15 )) , " 6.1...
W09 OK 126.4 m\bounded_area(sin(2x), cos(x), x, 0, 2pi) m\bounded_area(sin(2x),cos(x),x,0,2π) m\bounded_area(sin(2x),cos(x),x,0,2π) M1: ∫[ 0 , (( π )/( 6 )) ] (g-f)= (( 1 )/( 4 )) M1: ∫[ (( π )/( 6 )) , (( π )/( 2 )) ] (f-g)= (( 1 )/( 4 )) M1: ∫[ (( π )/( 2 )) , (( 5*π )/( 6 )) ] (g-f)= (( 1 )/( 4 )) M1: ∫[...
W10 OK 44.2 m\integ_by_recog((x^2+2x)e^(-x), x^2*e^(-x), x, 0, 2) m\integ_by_recog((x^2+2x)e^(−x),x^2e^(−x),x,0,2) m\integ_by_recog((x^(2)+2x)e^(−x),x^(2)e^(−x),x,0,2) M1: F'(x)=( −1 )g+( (( 2 )/( e ^( x ) )) ) ∫g dx= (( −x ^( 2 ) -2x-2 )/( e ^( x ) )) +c [[ " " , " Exact " , " 4dp " ][ " c1, h " , −1 , (( 2 )/( e...
W11 OK 46.9 m\integ_by_recog(xln(2x), ln(2*x), x, 1, e) m\integ_by_recog(xln(2x),ln(2x),x,1,e) m\integ_by_recog(xln(2x),ln(2x),x,1,e) M1: F'(x)=( 1 )g+( 1 ) ∫g dx= xln ( x ) + ( ln ( 2 ) -1 ) *x +c [[ " " , " Exact " , " 4dp " ][ " c1, h " , 1 , 1 ][ " ΔF(x) " , ln ( 2 ) * ( e-1 ) +e , " 3.9093 " ][ " ∫h...
W12 OK 54.5 m\cont_pdf_stats(2e^(-2x), x, 0, infinity) m\cont_pdf_stats(2e^(−2x),x,0,∞) m\cont_pdf_stats(2e^(−2x),x,0,∞) M1 E(X)=∫_[ 0 , ∞ ]xf= (( 1 )/( 2 )) M1 Var=∫x^2f-( (( 1 )/( 2 )) )^2= (( 1 )/( 4 )) [[ " " , " Exact " , " 4dp " ][ " Area " , 1 , 1. ][ " E(X) " , (( 1 )/( 2 )) , 0.5 ][ " E(X^2) " , ...
W13 OK 64.1 m\cont_pdf_stats(e^(-x)/(1+e^(-x))^2, x, -infinity, infinity) m\cont_pdf_stats(e^(−x)/(1+e^(−x))^2,x,−∞,∞) m\cont_pdf_stats(((e^(−x))/((1+e^(−x))^(2))),x,−∞,∞) M1 E(X)=∫_[ −∞ , ∞ ]xf= 0 M1 Var=∫x^2f-( 0 )^2= (( 32898681336943 )/( 10000000000000 )) [[ " " , " Exact " , " 4dp " ][ " Area " , 1 , 1. ][ " E(X) " , 0 , 0...
W14 OK 36.8 m\inverse_func((2*x-3)/(x+4), x) m\inverse_func((2x-3)/(x+4),x) m\inverse_func(((2x-3)/(x+4)),x) M1: x=f(y), dom(f^-1)=ran(f) f^-1( x )= (( − ( 4*x+3 ) )/( x-2 )) [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {} " , " {} " ][ " f(x)=x " , " {} " , " {} " ]] 0 {} Done
W15 OK 40.6 m\inverse_func(2*(x-3)^5-4, x) m\inverse_func(2(x-3)^5-4,x) m\inverse_func(2(x-3)^(5)-4,x) M1: x=f(y), dom(f^-1)=ran(f) f^-1( x )= (( 2 ^( (( 4 )/( 5 )) ) * ( x+4 ) ^( (( 1 )/( 5 )) ) )/( 2 )) +3 [[ " Item " , " Exact " , " 4dp " ][ " f'=0 " , " {3} " , " {3.} " ][ " f(x)=x " , " Numer...
W16 OK 16.1 m\inv_intersect_k(√(x-k), x, k) m\inv_intersect_k(√(x-k),x,k) m\inv_intersect_k(√(x-k),x,k) [[ " Condition " , " Exact " , " Decimal " ][ " f=x, f'=1 " , x= (( 1 )/( 2 )) and k= (( 1 )/( 4 )) , x=0.5 and k=0.25 ][ " f=x, f'=-1 " , false , false ][ " f=x, f'=0 " , false , false ]] 0 {} Done
W17 OK 39.7 m\linear_sys_k(kx+2y=k, 2x+ky=2, x, y, k) m\linear_sys_k(kx+2y=k,2x+ky=2,x,y,k) m\linear_sys_k(kx+2y=k,2x+ky=2,x,y,k) M1 det: k ^( 2 ) -4 =0 [[ " Case " , " Exact k " , " 4dp " ][ " det=0 " , " {−2,2} " , " {−2.,2.} " ][ " Inf " , " {−2,2} " , " {−2.,2.} " ][ " None " , " {} " , " {} " ]] 0...
W18 OK 30.4 m\linear_sys_k(kx+ky=2*k, x+y=2, x, y, k) m\linear_sys_k(kx+ky=2k,x+y=2,x,y,k) m\linear_sys_k(kx+ky=2k,x+y=2,x,y,k) M1 det: 0 =0 [[ " Case " , " Exact k " , " 4dp " ][ " det=0 " , " All k∈R " , " All k∈R " ][ " Inf " , " All k∈R " , " All k∈R " ][ " None " , " {} " , " {} " ]] 0 {} Done
W19 OK 19.5 m\func_identities(ln(x-1), x) m\func_identities(ln(x-1),x) m\func_identities(ln(x-1),x) [[ " Identity " , " OK " , " Diff " ][ " f(x+y)=fx+fy " , " NO " , " 0.4234 " ][ " f(x+y)=fxfy " , " NO " , " 1.269 " ][ " f(xy)=fx+fy " , " NO " , " 0.7842 " ][ " f(xy)=fxfy " , " NO " , " 1.6299 ...
W20 OK 19.3 m\func_identities((x+2)/(x-1), x) m\func_identities((x+2)/(x-1),x) m\func_identities(((x+2)/(x-1)),x) [[ " Identity " , " OK " , " Diff " ][ " f(x+y)=fx+fy " , " NO " , " 1.5106 " ][ " f(x+y)=fxfy " , " NO " , " −11.5717 " ][ " f(xy)=fx+fy " , " NO " , " 3.3885 " ][ " f(xy)=fxfy " , " NO ...
W21 OK 31.9 m\num_solutions_k(x*e^(-x), x, 0, infinity) m\num_solutions_k(xe^(−x),x,0,∞) m\num_solutions_k(xe^(−x),x,0,∞) k_crit= { 0,e ^( −1 ) } [[ " Range of k " , " Test " , " #Sol " ][ " k<0 " , " −1. " , 0 ][ " k=0 " , " 0. " , 1 ][ " 0<ke^−1 ...
W22 OK 30.4 m\num_solutions_k(abs(x^2-4), x, -3, 3) m\num_solutions_k(abs(x^2-4),x,−3,3) m\num_solutions_k(abs(x^(2)-4),x,−3,3) k_crit= { 0,4,5 } [[ " Range of k " , " Test " , " #Sol " ][ " k<0 " , " −1. " , 0 ][ " k=0 " , " 0. " , 2 ][ " 0<k<4 " , " 2. " , 4 ][ " k=4 " , " 4. " , 3 ][ " 4<k<5 " , " 4.5 " ,...
W23 OK 50.4 m\binom_min_n(3, 0.15, 0.90) m\binom_min_n(3,0.15,0.9) m\binom_min_n(3,0.15,0.9) M1: Pr(X≥ 3 )≥ (( 9 )/( 10 )) p= (( 3 )/( 20 )) Min n= 34 [[ " n " , " Pr(X<k) " , " Pr(X≥k) " ][ 33 , " 0.109 " , " 0.891 " ][ 34 , " 0.0975 " , " 0.9025 " ]] 0 {} Done
W24 OK 50.4 m\interval_minmax(abs(x^2-4), x, -1, 3) m\interval_minmax(abs(x^2-4),x,−1,3) m\interval_minmax(abs(x^(2)-4),x,−1,3) M1: f'( x )= 2xsign ( x ^( 2 ) -4 ) =0 [[ " x " , " f(x) " , " x(4d) " , " y(4d) " , " Src " ][ −1 , 3 , " −1. " , " 3. " , " EndL " ][ 0 , 4 , " 0. " , " 4. " , " f'=0 " ][ 2 , 0...