Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • -x^2+4x+5
  • x^2+3x+3
  • x^2+3x-10
  • x^2-2x+2

  • Identical expressions

  • cos(x)*sin(x^ two)
  • co sinus of e of (x) multiply by sinus of (x squared )
  • co sinus of e of (x) multiply by sinus of (x to the power of two)
  • cos(x)*sin(x2)
  • cosx*sinx2
  • cos(x)*sin(x²)
  • cos(x)*sin(x to the power of 2)
  • cos(x)sin(x^2)
  • cos(x)sin(x2)
  • cosxsinx2
  • cosxsinx^2

  • Similar expressions

  • cosx*sin(x^2)
Plotting a function graph/ cos(x)*sin(x^2)

Graphing y = cos(x)*sin(x^2)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
                 / 2\
f(x) = cos(x)*sin\x /
f(x)=sin⁡(x2)cos⁡(x)f{\left(x \right)} = \sin{\left(x^{2} \right)} \cos{\left(x \right)} 
f = sin(x^2)*cos(x)
The graph of the function
02468-8-6-4-2-10102-2
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
sin⁡(x2)cos⁡(x)=0\sin{\left(x^{2} \right)} \cos{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Numerical solution
x1=−45.8103033454045x_{1} = -45.8103033454045
x2=−98.9562746936211x_{2} = -98.9562746936211
x3=−86.1602195936888x_{3} = -86.1602195936888
x4=−73.9349120324508x_{4} = -73.9349120324508
x5=−27.6298211145552x_{5} = -27.6298211145552
x6=−69.8490758065198x_{6} = -69.8490758065198
x7=3.96332729760601x_{7} = 3.96332729760601
x8=−91.9628589348098x_{8} = -91.9628589348098
x9=64.2499240996983x_{9} = 64.2499240996983
x10=−14.0684162995043x_{10} = -14.0684162995043
x11=59.8449298194288x_{11} = 59.8449298194288
x12=−92.6774746899941x_{12} = -92.6774746899941
x13=−51.8575289757704x_{13} = -51.8575289757704
x14=−48.9915991506973x_{14} = -48.9915991506973
x15=73.9986215763984x_{15} = 73.9986215763984
x16=94.1071181711013x_{16} = 94.1071181711013
x17=22.137941502317x_{17} = 22.137941502317
x18=−23.5142575266965x_{18} = -23.5142575266965
x19=28.2482660354898x_{19} = 28.2482660354898
x20=73.1875363321556x_{20} = 73.1875363321556
x21=10.7814158709709x_{21} = 10.7814158709709
x22=−29.8172889607005x_{22} = -29.8172889607005
x23=−89.7498945058111x_{23} = -89.7498945058111
x24=16.244807875181x_{24} = 16.244807875181
x25=8.1224039375905x_{25} = 8.1224039375905
x26=−58.0055663880172x_{26} = -58.0055663880172
x27=−31.2072703486357x_{27} = -31.2072703486357
x28=80.0945204032733x_{28} = 80.0945204032733
x29=−55.1173302693566x_{29} = -55.1173302693566
x30=61.2715531143107x_{30} = 61.2715531143107
x31=76.9690200129499x_{31} = 76.9690200129499
x32=−23.5619449019235x_{32} = -23.5619449019235
x33=10.6347231054331x_{33} = 10.6347231054331
x34=95.8109270062104x_{34} = 95.8109270062104
x35=−84.447707628146x_{35} = -84.447707628146
x36=−89.5396250380866x_{36} = -89.5396250380866
x37=14.1371669411541x_{37} = 14.1371669411541
x38=−36.3677124268396x_{38} = -36.3677124268396
x39=52.5794782701295x_{39} = 52.5794782701295
x40=77.5840932426103x_{40} = 77.5840932426103
x41=−11.7571287633483x_{41} = -11.7571287633483
x42=−5.87856438167413x_{42} = -5.87856438167413
x43=−15.7539144225679x_{43} = -15.7539144225679
x44=101.526181334807x_{44} = 101.526181334807
x45=58.1408092071534x_{45} = 58.1408092071534
x46=86.2331131935235x_{46} = 86.2331131935235
x47=98.1273737713015x_{47} = 98.1273737713015
x48=42.2052488985128x_{48} = 42.2052488985128
x49=0x_{49} = 0
x50=82.2235209081029x_{50} = 82.2235209081029
x51=89.5571663498502x_{51} = 89.5571663498502
x52=−391.210720344267x_{52} = -391.210720344267
x53=−22.0668724858422x_{53} = -22.0668724858422
x54=−65.6765309176633x_{54} = -65.6765309176633
x55=−9.86860538583257x_{55} = -9.86860538583257
x56=36.1511070908396x_{56} = 36.1511070908396
x57=−61.261056745001x_{57} = -61.261056745001
x58=66.2006174575265x_{58} = 66.2006174575265
x59=−64.2743676707175x_{59} = -64.2743676707175
x60=−67.678963415037x_{60} = -67.678963415037
x61=−23.8459277508708x_{61} = -23.8459277508708
x62=52.2498231190263x_{62} = 52.2498231190263
x63=39.2349385147855x_{63} = 39.2349385147855
x64=18.2485292908913x_{64} = 18.2485292908913
x65=−55.8815094433593x_{65} = -55.8815094433593
x66=−70.6540213049065x_{66} = -70.6540213049065
x67=20.209083229248x_{67} = 20.209083229248
x68=23.7799637856361x_{68} = 23.7799637856361
x69=−41.793845424846x_{69} = -41.793845424846
x70=46.3217851815086x_{70} = 46.3217851815086
x71=61.2971843863435x_{71} = 61.2971843863435
x72=−1.77245385090552x_{72} = -1.77245385090552
x73=83.6815990815881x_{73} = 83.6815990815881
x74=70.6984717788253x_{74} = 70.6984717788253
x75=6.13996024767893x_{75} = 6.13996024767893
x76=66.6263492885688x_{76} = 66.6263492885688
x77=78.9289441970977x_{77} = 78.9289441970977
x78=46.4234053076958x_{78} = 46.4234053076958
x79=−17.9009064202391x_{79} = -17.9009064202391
x80=−7.72594721818665x_{80} = -7.72594721818665
x81=30.079539295572x_{81} = 30.079539295572
x82=−95.8185759344887x_{82} = -95.8185759344887
x83=−43.8480866628973x_{83} = -43.8480866628973
x84=−34.139872209512x_{84} = -34.139872209512
x85=−59.9236214113694x_{85} = -59.9236214113694
x86=−19.8166364880301x_{86} = -19.8166364880301
x87=1.77245385090552x_{87} = 1.77245385090552
x88=39.1547853391105x_{88} = 39.1547853391105
x89=−25.8073176165412x_{89} = -25.8073176165412
x90=32.9867228626928x_{90} = 32.9867228626928
x91=−39.751994978311x_{91} = -39.751994978311
x92=45.535163899664x_{92} = 45.535163899664
x93=−77.5233303355659x_{93} = -77.5233303355659
x94=−33.862683274665x_{94} = -33.862683274665
x95=−76.8926353694292x_{95} = -76.8926353694292
x96=−3.96332729760601x_{96} = -3.96332729760601
x97=−98.9721470611453x_{97} = -98.9721470611453
x98=92.6769832808989x_{98} = 92.6769832808989
x99=54.9778714378214x_{99} = 54.9778714378214
x100=−83.8503688646267x_{100} = -83.8503688646267
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to cos(x)*sin(x^2).
sin⁡(02)cos⁡(0)\sin{\left(0^{2} \right)} \cos{\left(0 \right)}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
2xcos⁡(x)cos⁡(x2)−sin⁡(x)sin⁡(x2)=02 x \cos{\left(x \right)} \cos{\left(x^{2} \right)} - \sin{\left(x \right)} \sin{\left(x^{2} \right)} = 0
Solve this equation
The roots of this equation
x1=−21.7443208246461x_{1} = -21.7443208246461
x2=−57.6114316103265x_{2} = -57.6114316103265
x3=66.0699800161888x_{3} = 66.0699800161888
x4=56.175913886337x_{4} = 56.175913886337
x5=−54.2410486649869x_{5} = -54.2410486649869
x6=20.4309423892029x_{6} = 20.4309423892029
x7=−36.0818579563209x_{7} = -36.0818579563209
x8=29.829741482418x_{8} = 29.829741482418
x9=82.7850976847909x_{9} = 82.7850976847909
x10=78.1389021841115x_{10} = 78.1389021841115
x11=−10.957767460846x_{11} = -10.957767460846
x12=62.2002992999418x_{12} = 62.2002992999418
x13=−36.1766711135295x_{13} = -36.1766711135295
x14=98.967318895804x_{14} = 98.967318895804
x15=−14.0032317322368x_{15} = -14.0032317322368
x16=−42.0743813758713x_{16} = -42.0743813758713
x17=46.032869960288x_{17} = 46.032869960288
x18=64.3994668189113x_{18} = 64.3994668189113
x19=26.7041238409344x_{19} = 26.7041238409344
x20=−29.3120570723519x_{20} = -29.3120570723519
x21=22.3144555829732x_{21} = 22.3144555829732
x22=84.2894731854299x_{22} = 84.2894731854299
x23=−42.4203679035566x_{23} = -42.4203679035566
x24=−71.8554832810555x_{24} = -71.8554832810555
x25=42.1860239023499x_{25} = 42.1860239023499
x26=−16.0009491904737x_{26} = -16.0009491904737
x27=−53.7465455610153x_{27} = -53.7465455610153
x28=−67.6216177692932x_{28} = -67.6216177692932
x29=−62.0232911735757x_{29} = -62.0232911735757
x30=34.2088961514732x_{30} = 34.2088961514732
x31=51.8487347950227x_{31} = 51.8487347950227
x32=−79.8291866176748x_{32} = -79.8291866176748
x33=−23.749242427506x_{33} = -23.749242427506
x34=7.7808229418531x_{34} = 7.7808229418531
x35=−62.8784063418455x_{35} = -62.8784063418455
x36=4.70091565676332x_{36} = 4.70091565676332
x37=26.259086539065x_{37} = 26.259086539065
x38=10.2562149360732x_{38} = 10.2562149360732
x39=36.1408978109486x_{39} = 36.1408978109486
x40=−3.74766067133477x_{40} = -3.74766067133477
x41=82.461938457206x_{41} = 82.461938457206
x42=60.2503535867024x_{42} = 60.2503535867024
x43=−26.4373808099425x_{43} = -26.4373808099425
x44=61.1809301963892x_{44} = 61.1809301963892
x45=18.0328686012482x_{45} = 18.0328686012482
x46=−65.8556721673776x_{46} = -65.8556721673776
x47=−33.7001911481362x_{47} = -33.7001911481362
x48=−51.7503243924615x_{48} = -51.7503243924615
x49=94.8966350594679x_{49} = 94.8966350594679
x50=86.7145856729587x_{50} = 86.7145856729587
x51=96.0811603317475x_{51} = 96.0811603317475
x52=23.6214725471253x_{52} = 23.6214725471253
x53=0x_{53} = 0
x54=90.3169469354969x_{54} = 90.3169469354969
x55=−92.8385290764838x_{55} = -92.8385290764838
x56=−71.0200484194458x_{56} = -71.0200484194458
x57=−47.9381265468237x_{57} = -47.9381265468237
x58=−45.5148417861163x_{58} = -45.5148417861163
x59=−44.0803123955744x_{59} = -44.0803123955744
x60=−85.8039257747406x_{60} = -85.8039257747406
x61=−1.67484432484861x_{61} = -1.67484432484861
x62=54.9762522924857x_{62} = 54.9762522924857
x63=−67.5251887322074x_{63} = -67.5251887322074
x64=51.8088129558038x_{64} = 51.8088129558038
x65=−95.8526961740184x_{65} = -95.8526961740184
x66=−98.8528049848859x_{66} = -98.8528049848859
x67=76.4315416810569x_{67} = 76.4315416810569
x68=39.3763165001392x_{68} = 39.3763165001392
x69=73.8280180700468x_{69} = 73.8280180700468
x70=4.13465262627828x_{70} = 4.13465262627828
x71=14.2458403046005x_{71} = 14.2458403046005
x72=15.9025787613332x_{72} = 15.9025787613332
x73=−83.972087632902x_{73} = -83.972087632902
x74=−8.22787376837475x_{74} = -8.22787376837475
x75=−97.7343881376139x_{75} = -97.7343881376139
x76=−93.881522316429x_{76} = -93.881522316429
x77=47.7411566321408x_{77} = 47.7411566321408
x78=−77.8367964156153x_{78} = -77.8367964156153
x79=−75.8125376133442x_{79} = -75.8125376133442
x80=−82.1183644934327x_{80} = -82.1183644934327
x81=6.26667579623329x_{81} = 6.26667579623329
x82=2.23412500791198x_{82} = 2.23412500791198
x83=−19.9339927192786x_{83} = -19.9339927192786
x84=−31.8794194517317x_{84} = -31.8794194517317
x85=−90.2995543164443x_{85} = -90.2995543164443
x86=−7.7808229418531x_{86} = -7.7808229418531
x87=99.0596546447822x_{87} = 99.0596546447822
x88=−59.6740765195264x_{88} = -59.6740765195264
x89=67.5251887322074x_{89} = 67.5251887322074
x90=92.634412032881x_{90} = 92.634412032881
x91=−55.8393982203108x_{91} = -55.8393982203108
x92=−81.8885110144078x_{92} = -81.8885110144078
x93=86.4081996571392x_{93} = 86.4081996571392
x94=−73.7952790938783x_{94} = -73.7952790938783
x95=37.536735170322x_{95} = 37.536735170322
x96=−17.2772507335565x_{96} = -17.2772507335565
x97=−5.7478922734498x_{97} = -5.7478922734498
x98=−17.7702721697402x_{98} = -17.7702721697402
x99=26.7424722578364x_{99} = 26.7424722578364
The values of the extrema at the points:
(-21.744320824646053, -0.969676097221814)

(-57.611431610326534, 0.486400074331572)

(66.0699800161888, 0.995343915349401)

(56.175913886337, 0.931322325891384)

(-54.24104866498691, -0.671903550807613)

(20.430942389202887, -0.00420586068706861)

(-36.081857956320945, -0.0445058898446669)

(29.829741482418022, 0.0104073009335254)

(82.78509768479086, -0.450273366645496)

(78.13890218411152, 0.920701233646281)

(-10.95776746084597, -0.0241222477221928)

(62.20029929994178, -0.80709718360807)

(-36.17667111352951, 0.046478368154231)

(98.96731889580397, -0.00583967022909107)

(-14.003231732236845, 0.129079844864294)

(-42.074381375871305, 0.330580102335346)

(46.032869960288, -0.461480368412829)

(64.39946681891129, 0.00120710383472745)

(26.704123840934372, -1.8349056647797e-5)

(-29.312057072351926, 0.507970255345382)

(22.314455582973224, -0.948163233336424)

(84.28947318542987, 0.861012663162526)

(-42.42036790355657, 0.00533064495466314)

(-71.85548328105554, 0.92060942237565)

(42.18602390234994, -0.223273371835521)

(-16.00094919047374, 0.957343240124375)

(-53.74654556101527, 0.942926043018534)

(-67.62161776929321, -0.0769493800481582)

(-62.02329117357569, 0.690514702163622)

(34.20889615147322, -0.93983071729092)

(51.84873479502273, 0.00984917104535034)

(-79.82918661767485, -0.27766072270618)

(-23.749242427506, -0.185065957824233)

(7.780822941853101, -0.0549592504575931)

(-62.87840634184554, 0.998916523665929)

(4.700915656763321, 0.00123051841008508)

(26.25908653906497, -0.42961903305635)

(10.256214936073231, 0.672853864692745)

(36.14089781094858, -0.00846572461553774)

(-3.7476606713347747, -0.818402772365498)

(82.46193845720597, 0.7105282681268)

(60.25035358670237, 0.847194146133567)

(-26.437380809942546, 0.262394827342632)

(61.180930196389205, 0.0796294820628317)

(18.032868601248204, -0.684341420447224)

(-65.85567216737758, -0.993072306512991)

(-33.700191148136184, 0.654363939152423)

(-51.75032439246152, 0.0853139441750081)

(94.89663505946787, 0.796769580838193)

(86.71458567295866, -0.315266706524861)

(96.08116033174753, -0.259528591129436)

(23.62147254712529, -0.0560615995086132)

(0, 0)

(90.31694693549686, -0.704374006726898)

(-92.83852907648381, -0.160756304643403)

(-71.02004841944581, 0.327959090743256)

(-47.938126546823675, 0.686381734150551)

(-45.514841786116335, -0.0367579709104531)

(-44.080312395574445, 0.995199731182475)

(-85.8039257747406, 0.556233746167078)

(-1.674844324848613, -0.0342921123704619)

(54.976252292485654, -0.000283792846225007)

(-67.52518873220743, 0.0177585582888914)

(51.808812955803766, 0.0259101624261079)

(-95.8526961740184, -0.0337221111406507)

(-98.85280498488589, -0.10703965101645)

(76.4315416810569, -0.511940665927364)

(39.37631650013918, 0.10546498949545)

(73.82801807004678, 5.1328095717406e-5)

(4.134652626278284, 0.5369693932868)

(14.245840304600469, -0.103248603871224)

(15.902578761333166, -0.981103260528867)

(-83.97208763290197, -0.659280989408808)

(-8.22787376837475, 0.360937712244325)

(-97.73438813761395, -0.941068492535655)

(-93.88152231642897, -0.933672285597302)

(47.741156632140836, 0.815440953086963)

(-77.83679641561532, -0.762881909929572)

(-75.81253761334425, -0.915388872550898)

(-82.11836449343274, 0.906040577000121)

(6.266675796233288, 0.999862853512404)

(2.234125007911981, 0.591945725863939)

(-19.933992719278617, 0.466885578466679)

(-31.879419451731668, -0.894468878964384)

(-90.29955431644433, 0.691921908953395)

(-7.780822941853101, -0.0549592504575931)

(99.05965464478224, -0.0991952820278843)

(-59.6740765195264, 0.999869034375718)

(67.52518873220743, 0.0177585582888914)

(92.63441203288097, 0.0422207914789287)

(-55.839398220310784, 0.758815401718861)

(-81.8885110144078, 0.978630114019052)

(86.40819965713925, 0.0133630181218172)

(-73.79527909387828, 0.0314522513610657)

(37.536735170321954, 0.986843498791729)

(-17.27725073355649, 7.85622449909438e-5)

(-5.747892273449797, 0.85897692575953)

(-17.770272169740206, 0.471309393582847)

(26.74247225783638, 0.0350921057346341)


Intervals of increase and decrease of the function:
Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
Minima of the function at points:
x1=−21.7443208246461x_{1} = -21.7443208246461
x2=−54.2410486649869x_{2} = -54.2410486649869
x3=20.4309423892029x_{3} = 20.4309423892029
x4=−36.0818579563209x_{4} = -36.0818579563209
x5=82.7850976847909x_{5} = 82.7850976847909
x6=−10.957767460846x_{6} = -10.957767460846
x7=62.2002992999418x_{7} = 62.2002992999418
x8=98.967318895804x_{8} = 98.967318895804
x9=46.032869960288x_{9} = 46.032869960288
x10=26.7041238409344x_{10} = 26.7041238409344
x11=22.3144555829732x_{11} = 22.3144555829732
x12=42.1860239023499x_{12} = 42.1860239023499
x13=−67.6216177692932x_{13} = -67.6216177692932
x14=34.2088961514732x_{14} = 34.2088961514732
x15=−79.8291866176748x_{15} = -79.8291866176748
x16=−23.749242427506x_{16} = -23.749242427506
x17=7.7808229418531x_{17} = 7.7808229418531
x18=26.259086539065x_{18} = 26.259086539065
x19=36.1408978109486x_{19} = 36.1408978109486
x20=−3.74766067133477x_{20} = -3.74766067133477
x21=18.0328686012482x_{21} = 18.0328686012482
x22=−65.8556721673776x_{22} = -65.8556721673776
x23=86.7145856729587x_{23} = 86.7145856729587
x24=96.0811603317475x_{24} = 96.0811603317475
x25=23.6214725471253x_{25} = 23.6214725471253
x26=0x_{26} = 0
x27=90.3169469354969x_{27} = 90.3169469354969
x28=−92.8385290764838x_{28} = -92.8385290764838
x29=−45.5148417861163x_{29} = -45.5148417861163
x30=−1.67484432484861x_{30} = -1.67484432484861
x31=54.9762522924857x_{31} = 54.9762522924857
x32=−95.8526961740184x_{32} = -95.8526961740184
x33=−98.8528049848859x_{33} = -98.8528049848859
x34=76.4315416810569x_{34} = 76.4315416810569
x35=14.2458403046005x_{35} = 14.2458403046005
x36=15.9025787613332x_{36} = 15.9025787613332
x37=−83.972087632902x_{37} = -83.972087632902
x38=−97.7343881376139x_{38} = -97.7343881376139
x39=−93.881522316429x_{39} = -93.881522316429
x40=−77.8367964156153x_{40} = -77.8367964156153
x41=−75.8125376133442x_{41} = -75.8125376133442
x42=−31.8794194517317x_{42} = -31.8794194517317
x43=−7.7808229418531x_{43} = -7.7808229418531
x44=99.0596546447822x_{44} = 99.0596546447822
Maxima of the function at points:
x44=−57.6114316103265x_{44} = -57.6114316103265
x44=66.0699800161888x_{44} = 66.0699800161888
x44=56.175913886337x_{44} = 56.175913886337
x44=29.829741482418x_{44} = 29.829741482418
x44=78.1389021841115x_{44} = 78.1389021841115
x44=−36.1766711135295x_{44} = -36.1766711135295
x44=−14.0032317322368x_{44} = -14.0032317322368
x44=−42.0743813758713x_{44} = -42.0743813758713
x44=64.3994668189113x_{44} = 64.3994668189113
x44=−29.3120570723519x_{44} = -29.3120570723519
x44=84.2894731854299x_{44} = 84.2894731854299
x44=−42.4203679035566x_{44} = -42.4203679035566
x44=−71.8554832810555x_{44} = -71.8554832810555
x44=−16.0009491904737x_{44} = -16.0009491904737
x44=−53.7465455610153x_{44} = -53.7465455610153
x44=−62.0232911735757x_{44} = -62.0232911735757
x44=51.8487347950227x_{44} = 51.8487347950227
x44=−62.8784063418455x_{44} = -62.8784063418455
x44=4.70091565676332x_{44} = 4.70091565676332
x44=10.2562149360732x_{44} = 10.2562149360732
x44=82.461938457206x_{44} = 82.461938457206
x44=60.2503535867024x_{44} = 60.2503535867024
x44=−26.4373808099425x_{44} = -26.4373808099425
x44=61.1809301963892x_{44} = 61.1809301963892
x44=−33.7001911481362x_{44} = -33.7001911481362
x44=−51.7503243924615x_{44} = -51.7503243924615
x44=94.8966350594679x_{44} = 94.8966350594679
x44=−71.0200484194458x_{44} = -71.0200484194458
x44=−47.9381265468237x_{44} = -47.9381265468237
x44=−44.0803123955744x_{44} = -44.0803123955744
x44=−85.8039257747406x_{44} = -85.8039257747406
x44=−67.5251887322074x_{44} = -67.5251887322074
x44=51.8088129558038x_{44} = 51.8088129558038
x44=39.3763165001392x_{44} = 39.3763165001392
x44=73.8280180700468x_{44} = 73.8280180700468
x44=4.13465262627828x_{44} = 4.13465262627828
x44=−8.22787376837475x_{44} = -8.22787376837475
x44=47.7411566321408x_{44} = 47.7411566321408
x44=−82.1183644934327x_{44} = -82.1183644934327
x44=6.26667579623329x_{44} = 6.26667579623329
x44=2.23412500791198x_{44} = 2.23412500791198
x44=−19.9339927192786x_{44} = -19.9339927192786
x44=−90.2995543164443x_{44} = -90.2995543164443
x44=−59.6740765195264x_{44} = -59.6740765195264
x44=67.5251887322074x_{44} = 67.5251887322074
x44=92.634412032881x_{44} = 92.634412032881
x44=−55.8393982203108x_{44} = -55.8393982203108
x44=−81.8885110144078x_{44} = -81.8885110144078
x44=86.4081996571392x_{44} = 86.4081996571392
x44=−73.7952790938783x_{44} = -73.7952790938783
x44=37.536735170322x_{44} = 37.536735170322
x44=−17.2772507335565x_{44} = -17.2772507335565
x44=−5.7478922734498x_{44} = -5.7478922734498
x44=−17.7702721697402x_{44} = -17.7702721697402
x44=26.7424722578364x_{44} = 26.7424722578364
Decreasing at intervals
[99.0596546447822,∞)\left[99.0596546447822, \infty\right)
Increasing at intervals
(−∞,−98.8528049848859]\left(-\infty, -98.8528049848859\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(sin⁡(x2)cos⁡(x))=⟨−1,1⟩\lim_{x \to -\infty}\left(\sin{\left(x^{2} \right)} \cos{\left(x \right)}\right) = \left\langle -1, 1\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞(sin⁡(x2)cos⁡(x))=⟨−1,1⟩\lim_{x \to \infty}\left(\sin{\left(x^{2} \right)} \cos{\left(x \right)}\right) = \left\langle -1, 1\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of cos(x)*sin(x^2), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(sin⁡(x2)cos⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x^{2} \right)} \cos{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(sin⁡(x2)cos⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x^{2} \right)} \cos{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
sin⁡(x2)cos⁡(x)=sin⁡(x2)cos⁡(x)\sin{\left(x^{2} \right)} \cos{\left(x \right)} = \sin{\left(x^{2} \right)} \cos{\left(x \right)}
- Yes
sin⁡(x2)cos⁡(x)=−sin⁡(x2)cos⁡(x)\sin{\left(x^{2} \right)} \cos{\left(x \right)} = - \sin{\left(x^{2} \right)} \cos{\left(x \right)}
- No
so, the function
is
even
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