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Trazado el gráfico de la función/ sin(x)-cos(x^2)+(1/4)

Gráfico de la función y = sin(x)-cos(x^2)+(1/4)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                   / 2\   1
f(x) = sin(x) - cos\x / + -
                          4
f(x)=(sin⁡(x)−cos⁡(x2))+14f{\left(x \right)} = \left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4} 
f = sin(x) - cos(x^2) + 1/4
Gráfico de la función
02468-8-6-4-2-10105-5
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
(sin⁡(x)−cos⁡(x2))+14=0\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=40.1111824792713x_{1} = 40.1111824792713
x2=−43.4238638224173x_{2} = -43.4238638224173
x3=−9.65261285774575x_{3} = -9.65261285774575
x4=−33.6919704330286x_{4} = -33.6919704330286
x5=−78.6622401239618x_{5} = -78.6622401239618
x6=90.9385101983754x_{6} = 90.9385101983754
x7=54.3623963985464x_{7} = 54.3623963985464
x8=−27.9964832675147x_{8} = -27.9964832675147
x9=−69.7503172817115x_{9} = -69.7503172817115
x10=43.3212314723419x_{10} = 43.3212314723419
x11=0.691602448121161x_{11} = 0.691602448121161
x12=−85.2944255047074x_{12} = -85.2944255047074
x13=73.876051319832x_{13} = 73.876051319832
x14=6.24917558715415x_{14} = 6.24917558715415
x15=6.69651557104387x_{15} = 6.69651557104387
x16=−24.7044915641557x_{16} = -24.7044915641557
x17=35.5686851346348x_{17} = 35.5686851346348
x18=25.4584447108766x_{18} = 25.4584447108766
x19=−90.0071782775614x_{19} = -90.0071782775614
x20=21.8260959682456x_{20} = 21.8260959682456
x21=−21.8848905883197x_{21} = -21.8848905883197
x22=68.2643913788867x_{22} = 68.2643913788867
x23=169.844666479171x_{23} = 169.844666479171
x24=−22.1635753055404x_{24} = -22.1635753055404
x25=2.42010171228507x_{25} = 2.42010171228507
x26=77.7441722010558x_{26} = 77.7441722010558
x27=98.2500719411958x_{27} = 98.2500719411958
x28=−3.64841219611475x_{28} = -3.64841219611475
x29=−25.9689454826438x_{29} = -25.9689454826438
x30=−26.9248773198902x_{30} = -26.9248773198902
x31=34.0823189250325x_{31} = 34.0823189250325
x32=12.8221133045797x_{32} = 12.8221133045797
x33=−47.7516263856737x_{33} = -47.7516263856737
x34=−83.7139403250785x_{34} = -83.7139403250785
x35=−1.55520891280466x_{35} = -1.55520891280466
x36=−59.7503539523153x_{36} = -59.7503539523153
x37=40.9764116446742x_{37} = 40.9764116446742
x38=75.5244784928168x_{38} = 75.5244784928168
x39=−11.7485351246587x_{39} = -11.7485351246587
x40=−68.4142549325336x_{40} = -68.4142549325336
x41=−90.8892327693225x_{41} = -90.8892327693225
x42=72.2496786240861x_{42} = 72.2496786240861
x43=68.2491628376529x_{43} = 68.2491628376529
x44=−83.385133658414x_{44} = -83.385133658414
x45=−53.7697549442524x_{45} = -53.7697549442524
x46=−10.05512490128x_{46} = -10.05512490128
x47=30.2496446403622x_{47} = 30.2496446403622
x48=−71.8104575408252x_{48} = -71.8104575408252
x49=28.0065685403739x_{49} = 28.0065685403739
x50=−77.8794998506028x_{50} = -77.8794998506028
x51=−97.5392361785001x_{51} = -97.5392361785001
x52=879.359550496925x_{52} = 879.359550496925
x53=−1.99782462685321x_{53} = -1.99782462685321
x54=−21.8180927772482x_{54} = -21.8180927772482
x55=99.8040429118756x_{55} = 99.8040429118756
x56=4.0847382487479x_{56} = 4.0847382487479
x57=−108.268255492474x_{57} = -108.268255492474
x58=10.2347083141931x_{58} = 10.2347083141931
x59=−18.5625074499192x_{59} = -18.5625074499192
x60=37.4528358578611x_{60} = 37.4528358578611
x61=367.362811896333x_{61} = 367.362811896333
x62=65.5028621304597x_{62} = 65.5028621304597
x63=29.5130989528393x_{63} = 29.5130989528393
x64=87.9748646153398x_{64} = 87.9748646153398
x65=16.0000573107138x_{65} = 16.0000573107138
x66=−24.4413856207385x_{66} = -24.4413856207385
x67=91.042700967986x_{67} = 91.042700967986
x68=−70.7821345465067x_{68} = -70.7821345465067
x69=94.3172556650567x_{69} = 94.3172556650567
x70=75.2503680674066x_{70} = 75.2503680674066
x71=82.3790523264691x_{71} = 82.3790523264691
x72=−65.7124580075391x_{72} = -65.7124580075391
x73=−45.4396168381865x_{73} = -45.4396168381865
x74=48.9030352869289x_{74} = 48.9030352869289
x75=−55.9999908638865x_{75} = -55.9999908638865
x76=−7.77289829567417x_{76} = -7.77289829567417
x77=25.6982715775585x_{77} = 25.6982715775585
x78=50.8848029425982x_{78} = 50.8848029425982
x79=37.7494005448309x_{79} = 37.7494005448309
x80=−88.5267746421002x_{80} = -88.5267746421002
x81=−93.9621491488001x_{81} = -93.9621491488001
x82=−39.819348570996x_{82} = -39.819348570996
x83=−57.3069117873017x_{83} = -57.3069117873017
x84=35.5945980633381x_{84} = 35.5945980633381
x85=8.99137215079902x_{85} = 8.99137215079902
x86=106.101278877099x_{86} = 106.101278877099
x87=23.829670676031x_{87} = 23.829670676031
x88=61.0083417543066x_{88} = 61.0083417543066
x89=−43.9055787200602x_{89} = -43.9055787200602
x90=13.2449784557428x_{90} = 13.2449784557428
x91=−37.7847675885331x_{91} = -37.7847675885331
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en sin(x) - cos(x^2) + 1/4.
(−cos⁡(02)+sin⁡(0))+14\left(- \cos{\left(0^{2} \right)} + \sin{\left(0 \right)}\right) + \frac{1}{4}
Resultado:
f(0)=−34f{\left(0 \right)} = - \frac{3}{4}
Punto:
(0, -3/4)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
2xsin⁡(x2)+cos⁡(x)=02 x \sin{\left(x^{2} \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=22.349323885059x_{1} = 22.349323885059
x2=−47.4608457084011x_{2} = -47.4608457084011
x3=−22.4903520904245x_{3} = -22.4903520904245
x4=6.3967526067572x_{4} = 6.3967526067572
x5=56.2735892190937x_{5} = 56.2735892190937
x6=96.0892263352259x_{6} = 96.0892263352259
x7=−99.1940994186411x_{7} = -99.1940994186411
x8=42.2424741036786x_{8} = 42.2424741036786
x9=52.2497863224473x_{9} = 52.2497863224473
x10=−43.8482155265515x_{10} = -43.8482155265515
x11=−7.72541014397883x_{11} = -7.72541014397883
x12=−19.816274863823x_{12} = -19.816274863823
x13=90.6554540354125x_{13} = 90.6554540354125
x14=−0.730978270667906x_{14} = -0.730978270667906
x15=−9.87092112794122x_{15} = -9.87092112794122
x16=28.2485792398582x_{16} = 28.2485792398582
x17=14.7224702337865x_{17} = 14.7224702337865
x18=−41.8314912305025x_{18} = -41.8314912305025
x19=98.0953333197619x_{19} = 98.0953333197619
x20=−74.0622869224726x_{20} = -74.0622869224726
x21=87.7857185656868x_{21} = 87.7857185656868
x22=−81.840586323002x_{22} = -81.840586323002
x23=−5.87191528001199x_{23} = -5.87191528001199
x24=87.8035463465879x_{24} = 87.8035463465879
x25=66.3427786515794x_{25} = 66.3427786515794
x26=−72.1935532053449x_{26} = -72.1935532053449
x27=−77.7257170387604x_{27} = -77.7257170387604
x28=−83.9440058712679x_{28} = -83.9440058712679
x29=64.2499148858234x_{29} = 64.2499148858234
x30=16.2456215982105x_{30} = 16.2456215982105
x31=−61.8584222114262x_{31} = -61.8584222114262
x32=−39.7914116037745x_{32} = -39.7914116037745
x33=18.2479103002405x_{33} = 18.2479103002405
x34=69.3298616312379x_{34} = 69.3298616312379
x35=93.7559147144186x_{35} = 93.7559147144186
x36=−53.8778557584569x_{36} = -53.8778557584569
x37=8.12140237825279x_{37} = 8.12140237825279
x38=29.2322260727598x_{38} = 29.2322260727598
x39=1.75748767956681x_{39} = 1.75748767956681
x40=79.7604098082138x_{40} = 79.7604098082138
x41=−3.97400948361753x_{41} = -3.97400948361753
x42=27.2863953811205x_{42} = 27.2863953811205
x43=82.2044467599582x_{43} = 82.2044467599582
x44=60.885813954976x_{44} = 60.885813954976
x45=−15.3508947858058x_{45} = -15.3508947858058
x46=11.0691206807264x_{46} = 11.0691206807264
x47=−15.7549206941732x_{47} = -15.7549206941732
x48=47.2616324020612x_{48} = 47.2616324020612
x49=46.1858745664205x_{49} = 46.1858745664205
x50=−33.8628507747295x_{50} = -33.8628507747295
x51=−46.928316630699x_{51} = -46.928316630699
x52=−1.78948236293348x_{52} = -1.78948236293348
x53=−65.5808461895275x_{53} = -65.5808461895275
x54=−51.1560410192306x_{54} = -51.1560410192306
x55=36.7972126661047x_{55} = 36.7972126661047
x56=−91.9286709217352x_{56} = -91.9286709217352
x57=22.1384461152026x_{57} = 22.1384461152026
x58=6.13338537866179x_{58} = 6.13338537866179
x59=−87.1571856052754x_{59} = -87.1571856052754
x60=3.95230187084535x_{60} = 3.95230187084535
x61=85.4278345722129x_{61} = 85.4278345722129
x62=57.5433221417068x_{62} = 57.5433221417068
x63=−89.7498878995054x_{63} = -89.7498878995054
x64=48.1833155017359x_{64} = 48.1833155017359
x65=78.44981619248x_{65} = 78.44981619248
x66=−72.106467795218x_{66} = -72.106467795218
x67=9.71067451011131x_{67} = 9.71067451011131
x68=−11.621672446497x_{68} = -11.621672446497
x69=−40.1453184602676x_{69} = -40.1453184602676
x70=−17.9879387647864x_{70} = -17.9879387647864
x71=−89.8897901584974x_{71} = -89.8897901584974
x72=−14.0683294162172x_{72} = -14.0683294162172
x73=−22.0673844234238x_{73} = -22.0673844234238
x74=99.6364875148062x_{74} = 99.6364875148062
x75=44.7697244998911x_{75} = 44.7697244998911
x76=80.3686064857456x_{76} = 80.3686064857456
x77=94.1405234555763x_{77} = 94.1405234555763
x78=31.2578168207404x_{78} = 31.2578168207404
x79=−49.2792605670951x_{79} = -49.2792605670951
x80=−55.8533314248926x_{80} = -55.8533314248926
x81=57.7341585233858x_{81} = 57.7341585233858
x82=−95.8600997718734x_{82} = -95.8600997718734
Signos de extremos en los puntos:
(22.34932388505898, 0.899214550998202)

(-47.46084570840113, 1.58056628769818)

(-22.490352090424498, 1.7285358978664)

(6.396752606757205, 1.36030314711518)

(56.27358921909367, -1.02158596885626)

(96.08922633522592, 2.21359624249138)

(-99.19409941864106, 0.222763416653808)

(42.242474103678596, -1.73574697954699)

(52.24978632244733, 2.16570965376942)

(-43.848215526551456, -0.616255911808996)

(-7.725410143978831, 0.258219501823969)

(-19.816274863823022, 0.426870799296581)

(90.65545403541253, -0.31436230477943)

(-0.7309782706679064, -1.27820871872329)

(-9.87092112794122, 1.68044483800528)

(28.24857923985821, -0.724091651171351)

(14.722470233786547, 2.0833685437479)

(-41.831491230502486, 2.08643593813823)

(98.09533331976195, 0.601226993957887)

(-74.06228692247262, 0.222548265536392)

(87.78571856568684, 1.07206093361989)

(-81.84058632300203, -0.908487796295731)

(-5.871915280011989, 1.64672316794882)

(87.8035463465879, -0.910336890591339)

(66.34277865157937, 0.888981880025799)

(-72.19355320534488, 1.18694010507801)

(-77.72571703876044, 0.522882705493363)

(-83.94400587126786, 0.479894133412259)

(64.2499148858234, 0.23835944207481)

(16.24562159821051, -1.26177664427882)

(-61.85842221142619, 0.0768306534387587)

(-39.79141160377455, -1.61705157908055)

(18.24791030024052, -1.3157447333335)

(69.32986163123788, -0.536800429133705)

(93.75591471441857, -1.22225947668199)

(-53.87785575845691, -0.296383649424088)

(8.121402378252785, 2.21432331894488)

(29.23222607275975, -1.56793247208485)

(1.757487679566813, 2.23122856178744)

(79.76040980821381, 0.310694553304226)

(-3.9740094836175293, 1.98596791565122)

(27.286395381120506, 2.08484221611745)

(82.20444675995824, 1.74950019091033)

(60.88581395497595, -1.68041413795555)

(-15.3508947858058, 0.900005123632314)

(11.069120680726392, 0.252697808719373)

(-15.754920694173173, 1.29643756401958)

(47.26163240206123, 1.1126376460065)

(46.18587456642046, 2.05636542658033)

(-33.8628507747295, 0.609804928108061)

(-46.92831663069898, 1.05561656898399)

(-1.7894823629334766, 0.271977728650254)

(-65.58084618952749, 0.867383727832319)

(-51.15604101923061, 0.472557911280981)

(36.79721266610471, 0.465458455391031)

(-91.92867092173525, -0.0171549645821363)

(22.138446115202626, -0.89651589398298)

(6.13338537866179, -0.895986177863084)

(-87.15718560527543, -0.0274940903763204)

(3.9523018708453495, 0.521418115405953)

(85.42783457221287, 0.68136376085504)

(57.54332214170678, 0.0885819277160163)

(-89.74988789950542, -1.72708282333138)

(48.183315501735876, 0.377912527419599)

(78.44981619247996, 1.33985854897891)

(-72.10646779521804, 1.10037696142293)

(9.710674510111312, -1.03079681074621)

(-11.621672446496989, 2.06000225359449)

(-40.145318460267575, 0.609272386516736)

(-17.98793876478641, 2.00873282272673)

(-89.88979015849739, -1.6878531739228)

(-14.068329416217198, 0.252365378903732)

(-22.067384423423757, 1.32590679062373)

(99.63648751480619, -1.52987714544096)

(44.76972449989114, -0.0414287677900198)

(80.36860648574562, -1.71690252331832)

(94.1405234555763, 1.14293543038608)

(31.257816820740402, 1.09242344557681)

(-49.27926056709511, 2.08393133091633)

(-55.85333142489263, 1.89062010610832)

(57.73415852338577, 2.17667833321499)

(-95.86009977187342, 0.25086196722793)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=56.2735892190937x_{1} = 56.2735892190937
x2=−99.1940994186411x_{2} = -99.1940994186411
x3=42.2424741036786x_{3} = 42.2424741036786
x4=−43.8482155265515x_{4} = -43.8482155265515
x5=90.6554540354125x_{5} = 90.6554540354125
x6=−0.730978270667906x_{6} = -0.730978270667906
x7=28.2485792398582x_{7} = 28.2485792398582
x8=−74.0622869224726x_{8} = -74.0622869224726
x9=−81.840586323002x_{9} = -81.840586323002
x10=87.8035463465879x_{10} = 87.8035463465879
x11=64.2499148858234x_{11} = 64.2499148858234
x12=16.2456215982105x_{12} = 16.2456215982105
x13=−61.8584222114262x_{13} = -61.8584222114262
x14=−39.7914116037745x_{14} = -39.7914116037745
x15=18.2479103002405x_{15} = 18.2479103002405
x16=69.3298616312379x_{16} = 69.3298616312379
x17=93.7559147144186x_{17} = 93.7559147144186
x18=−53.8778557584569x_{18} = -53.8778557584569
x19=29.2322260727598x_{19} = 29.2322260727598
x20=60.885813954976x_{20} = 60.885813954976
x21=−91.9286709217352x_{21} = -91.9286709217352
x22=22.1384461152026x_{22} = 22.1384461152026
x23=6.13338537866179x_{23} = 6.13338537866179
x24=−87.1571856052754x_{24} = -87.1571856052754
x25=57.5433221417068x_{25} = 57.5433221417068
x26=−89.7498878995054x_{26} = -89.7498878995054
x27=9.71067451011131x_{27} = 9.71067451011131
x28=−89.8897901584974x_{28} = -89.8897901584974
x29=99.6364875148062x_{29} = 99.6364875148062
x30=44.7697244998911x_{30} = 44.7697244998911
x31=80.3686064857456x_{31} = 80.3686064857456
Puntos máximos de la función:
x31=22.349323885059x_{31} = 22.349323885059
x31=−47.4608457084011x_{31} = -47.4608457084011
x31=−22.4903520904245x_{31} = -22.4903520904245
x31=6.3967526067572x_{31} = 6.3967526067572
x31=96.0892263352259x_{31} = 96.0892263352259
x31=52.2497863224473x_{31} = 52.2497863224473
x31=−7.72541014397883x_{31} = -7.72541014397883
x31=−19.816274863823x_{31} = -19.816274863823
x31=−9.87092112794122x_{31} = -9.87092112794122
x31=14.7224702337865x_{31} = 14.7224702337865
x31=−41.8314912305025x_{31} = -41.8314912305025
x31=98.0953333197619x_{31} = 98.0953333197619
x31=87.7857185656868x_{31} = 87.7857185656868
x31=−5.87191528001199x_{31} = -5.87191528001199
x31=66.3427786515794x_{31} = 66.3427786515794
x31=−72.1935532053449x_{31} = -72.1935532053449
x31=−77.7257170387604x_{31} = -77.7257170387604
x31=−83.9440058712679x_{31} = -83.9440058712679
x31=8.12140237825279x_{31} = 8.12140237825279
x31=1.75748767956681x_{31} = 1.75748767956681
x31=79.7604098082138x_{31} = 79.7604098082138
x31=−3.97400948361753x_{31} = -3.97400948361753
x31=27.2863953811205x_{31} = 27.2863953811205
x31=82.2044467599582x_{31} = 82.2044467599582
x31=−15.3508947858058x_{31} = -15.3508947858058
x31=11.0691206807264x_{31} = 11.0691206807264
x31=−15.7549206941732x_{31} = -15.7549206941732
x31=47.2616324020612x_{31} = 47.2616324020612
x31=46.1858745664205x_{31} = 46.1858745664205
x31=−33.8628507747295x_{31} = -33.8628507747295
x31=−46.928316630699x_{31} = -46.928316630699
x31=−1.78948236293348x_{31} = -1.78948236293348
x31=−65.5808461895275x_{31} = -65.5808461895275
x31=−51.1560410192306x_{31} = -51.1560410192306
x31=36.7972126661047x_{31} = 36.7972126661047
x31=3.95230187084535x_{31} = 3.95230187084535
x31=85.4278345722129x_{31} = 85.4278345722129
x31=48.1833155017359x_{31} = 48.1833155017359
x31=78.44981619248x_{31} = 78.44981619248
x31=−72.106467795218x_{31} = -72.106467795218
x31=−11.621672446497x_{31} = -11.621672446497
x31=−40.1453184602676x_{31} = -40.1453184602676
x31=−17.9879387647864x_{31} = -17.9879387647864
x31=−14.0683294162172x_{31} = -14.0683294162172
x31=−22.0673844234238x_{31} = -22.0673844234238
x31=94.1405234555763x_{31} = 94.1405234555763
x31=31.2578168207404x_{31} = 31.2578168207404
x31=−49.2792605670951x_{31} = -49.2792605670951
x31=−55.8533314248926x_{31} = -55.8533314248926
x31=57.7341585233858x_{31} = 57.7341585233858
x31=−95.8600997718734x_{31} = -95.8600997718734
Decrece en los intervalos
[99.6364875148062,∞)\left[99.6364875148062, \infty\right)
Crece en los intervalos
(−∞,−99.1940994186411]\left(-\infty, -99.1940994186411\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((sin⁡(x)−cos⁡(x2))+14)=⟨−74,94⟩\lim_{x \to -\infty}\left(\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4}\right) = \left\langle - \frac{7}{4}, \frac{9}{4}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−74,94⟩y = \left\langle - \frac{7}{4}, \frac{9}{4}\right\rangle
lim⁡x→∞((sin⁡(x)−cos⁡(x2))+14)=⟨−74,94⟩\lim_{x \to \infty}\left(\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4}\right) = \left\langle - \frac{7}{4}, \frac{9}{4}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−74,94⟩y = \left\langle - \frac{7}{4}, \frac{9}{4}\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x) - cos(x^2) + 1/4, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((sin⁡(x)−cos⁡(x2))+14x)=0\lim_{x \to -\infty}\left(\frac{\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞((sin⁡(x)−cos⁡(x2))+14x)=0\lim_{x \to \infty}\left(\frac{\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
(sin⁡(x)−cos⁡(x2))+14=−sin⁡(x)−cos⁡(x2)+14\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4} = - \sin{\left(x \right)} - \cos{\left(x^{2} \right)} + \frac{1}{4}
- No
(sin⁡(x)−cos⁡(x2))+14=sin⁡(x)+cos⁡(x2)−14\left(\sin{\left(x \right)} - \cos{\left(x^{2} \right)}\right) + \frac{1}{4} = \sin{\left(x \right)} + \cos{\left(x^{2} \right)} - \frac{1}{4}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор