Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • sin(1/x)
  • 1/2x^4-4x^2+6
  • x*sin(x)^2
  • 3x^2 3x^2
  • Limit of the function:
  • x*sin(x)^2 x*sin(x)^2
  • Integral of d{x}:
  • x*sin(x)^2 x*sin(x)^2

  • Identical expressions

  • x*sin(x)^ two
  • x multiply by sinus of (x) squared
  • x multiply by sinus of (x) to the power of two
  • x*sin(x)2
  • x*sinx2
  • x*sin(x)²
  • x*sin(x) to the power of 2
  • xsin(x)^2
  • xsin(x)2
  • xsinx2
  • xsinx^2

  • Similar expressions

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

Graphing y = x*sin(x)^2

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
            2   
f(x) = x*sin (x)
f(x)=xsin⁡2(x)f{\left(x \right)} = x \sin^{2}{\left(x \right)} 
f = x*sin(x)^2
The graph of the function
02468-8-6-4-2-1010-2020
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:
xsin⁡2(x)=0x \sin^{2}{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=πx_{2} = \pi
Numerical solution
x1=−18.8495561496377x_{1} = -18.8495561496377
x2=87.964594335789x_{2} = 87.964594335789
x3=21.9911485852065x_{3} = 21.9911485852065
x4=3.14159299901751x_{4} = 3.14159299901751
x5=−59.6902604576978x_{5} = -59.6902604576978
x6=72.2566310277197x_{6} = 72.2566310277197
x7=25.1327410420105x_{7} = 25.1327410420105
x8=18.8495556906624x_{8} = 18.8495556906624
x9=12.5663704571697x_{9} = 12.5663704571697
x10=28.2743338652241x_{10} = 28.2743338652241
x11=94.2477796093525x_{11} = 94.2477796093525
x12=3.1415931516833x_{12} = 3.1415931516833
x13=37.6991120212708x_{13} = 37.6991120212708
x14=−12.5663703832991x_{14} = -12.5663703832991
x15=−21.9911485864645x_{15} = -21.9911485864645
x16=−31.4159267074656x_{16} = -31.4159267074656
x17=34.5575190322918x_{17} = 34.5575190322918
x18=−37.6991118772194x_{18} = -37.6991118772194
x19=3.1415923353488x_{19} = 3.1415923353488
x20=65.9734457529229x_{20} = 65.9734457529229
x21=−6.28318514963244x_{21} = -6.28318514963244
x22=−28.2743337190252x_{22} = -28.2743337190252
x23=3.69946911765974⋅10−5x_{23} = 3.69946911765974 \cdot 10^{-5}
x24=−87.964594358858x_{24} = -87.964594358858
x25=−3.14159271719906x_{25} = -3.14159271719906
x26=−15.7079632966406x_{26} = -15.7079632966406
x27=−81.6814090380603x_{27} = -81.6814090380603
x28=43.9822971694455x_{28} = 43.9822971694455
x29=−9.42477813384597x_{29} = -9.42477813384597
x30=50.2654824463527x_{30} = 50.2654824463527
x31=−18.8495557219808x_{31} = -18.8495557219808
x32=−3.14159295661011x_{32} = -3.14159295661011
x33=−43.9822971746086x_{33} = -43.9822971746086
x34=−65.97344576507x_{34} = -65.97344576507
x35=−9.09618852922⋅10−5x_{35} = -9.09618852922 \cdot 10^{-5}
x36=9.42477823217446x_{36} = 9.42477823217446
x37=6.28318528443896x_{37} = 6.28318528443896
x38=0x_{38} = 0
x39=15.7079634453651x_{39} = 15.7079634453651
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to x*sin(x)^2.
0sin⁡2(0)0 \sin^{2}{\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
2xsin⁡(x)cos⁡(x)+sin⁡2(x)=02 x \sin{\left(x \right)} \cos{\left(x \right)} + \sin^{2}{\left(x \right)} = 0
Solve this equation
The roots of this equation
x1=12.5663706143592x_{1} = 12.5663706143592
x2=78.5398163397448x_{2} = 78.5398163397448
x3=67.5516436614121x_{3} = 67.5516436614121
x4=86.3995849739529x_{4} = 86.3995849739529
x5=−65.9734457253857x_{5} = -65.9734457253857
x6=−86.3995849739529x_{6} = -86.3995849739529
x7=−15.707963267949x_{7} = -15.707963267949
x8=50.2654824574367x_{8} = 50.2654824574367
x9=81.6814089933346x_{9} = 81.6814089933346
x10=3.14159265358979x_{10} = 3.14159265358979
x11=20.4448034666183x_{11} = 20.4448034666183
x12=73.8341991854591x_{12} = 73.8341991854591
x13=23.5831433102848x_{13} = 23.5831433102848
x14=26.7222463741877x_{14} = 26.7222463741877
x15=−306.306916073247x_{15} = -306.306916073247
x16=14.1724320747999x_{16} = 14.1724320747999
x17=−75.398223686155x_{17} = -75.398223686155
x18=−42.4232862577008x_{18} = -42.4232862577008
x19=58.1280655761511x_{19} = 58.1280655761511
x20=−7.91705268466621x_{20} = -7.91705268466621
x21=56.5486677646163x_{21} = 56.5486677646163
x22=51.8459224452234x_{22} = 51.8459224452234
x23=−17.3076405374146x_{23} = -17.3076405374146
x24=−14.1724320747999x_{24} = -14.1724320747999
x25=15.707963267949x_{25} = 15.707963267949
x26=45.5640665961997x_{26} = 45.5640665961997
x27=1.83659720315213x_{27} = 1.83659720315213
x28=89.5409746049841x_{28} = 89.5409746049841
x29=7.91705268466621x_{29} = 7.91705268466621
x30=−73.8341991854591x_{30} = -73.8341991854591
x31=−59.6902604182061x_{31} = -59.6902604182061
x32=21.9911485751286x_{32} = 21.9911485751286
x33=6.28318530717959x_{33} = 6.28318530717959
x34=−87.9645943005142x_{34} = -87.9645943005142
x35=−28.2743338823081x_{35} = -28.2743338823081
x36=−67.5516436614121x_{36} = -67.5516436614121
x37=−9.42477796076938x_{37} = -9.42477796076938
x38=42.4232862577008x_{38} = 42.4232862577008
x39=59.6902604182061x_{39} = 59.6902604182061
x40=−83.2582106616487x_{40} = -83.2582106616487
x41=28.2743338823081x_{41} = 28.2743338823081
x42=94.2477796076938x_{42} = 94.2477796076938
x43=−29.861872403816x_{43} = -29.861872403816
x44=−72.2566310325652x_{44} = -72.2566310325652
x45=−84.8230016469244x_{45} = -84.8230016469244
x46=70.692907433161x_{46} = 70.692907433161
x47=−105.248104538899x_{47} = -105.248104538899
x48=−51.8459224452234x_{48} = -51.8459224452234
x49=−4.81584231784594x_{49} = -4.81584231784594
x50=−97.3893722612836x_{50} = -97.3893722612836
x51=37.6991118430775x_{51} = 37.6991118430775
x52=−50.2654824574367x_{52} = -50.2654824574367
x53=−94.2477796076938x_{53} = -94.2477796076938
x54=36.1421488970061x_{54} = 36.1421488970061
x55=−37.6991118430775x_{55} = -37.6991118430775
x56=−61.2692172687226x_{56} = -61.2692172687226
x57=−64.410411962776x_{57} = -64.410411962776
x58=−95.8237937978449x_{58} = -95.8237937978449
x59=−23.5831433102848x_{59} = -23.5831433102848
x60=−20.4448034666183x_{60} = -20.4448034666183
x61=−58.1280655761511x_{61} = -58.1280655761511
x62=−81.6814089933346x_{62} = -81.6814089933346
x63=43.9822971502571x_{63} = 43.9822971502571
x64=48.7049516666752x_{64} = 48.7049516666752
x65=−1.83659720315213x_{65} = -1.83659720315213
x66=−36.1421488970061x_{66} = -36.1421488970061
x67=−31.4159265358979x_{67} = -31.4159265358979
x68=0x_{68} = 0
x69=−39.2826357527234x_{69} = -39.2826357527234
x70=−21.9911485751286x_{70} = -21.9911485751286
x71=100.530964914873x_{71} = 100.530964914873
x72=34.5575191894877x_{72} = 34.5575191894877
x73=278.032748190065x_{73} = 278.032748190065
x74=65.9734457253857x_{74} = 65.9734457253857
x75=92.682377997352x_{75} = 92.682377997352
x76=−45.5640665961997x_{76} = -45.5640665961997
x77=80.1168534696549x_{77} = 80.1168534696549
x78=−53.4070751110265x_{78} = -53.4070751110265
x79=−89.5409746049841x_{79} = -89.5409746049841
x80=95.8237937978449x_{80} = 95.8237937978449
x81=−6.28318530717959x_{81} = -6.28318530717959
x82=25.1327412287183x_{82} = 25.1327412287183
x83=64.410411962776x_{83} = 64.410411962776
x84=−43.9822971502571x_{84} = -43.9822971502571
x85=72.2566310325652x_{85} = 72.2566310325652
x86=−80.1168534696549x_{86} = -80.1168534696549
x87=29.861872403816x_{87} = 29.861872403816
x88=87.9645943005142x_{88} = 87.9645943005142
The values of the extrema at the points:
(12.566370614359172, 3.01544596183035e-30)

(78.53981633974483, 1.8941914820334e-29)

(67.5516436614121, 67.5479429919577)

(86.3995849739529, 86.3966915384367)

(-65.97344572538566, -6.34844983898999e-29)

(-86.3995849739529, -86.3966915384367)

(-15.707963267948966, -5.8895428941999e-30)

(50.26548245743669, 1.92988541557142e-28)

(81.68140899333463, 1.25601110053315e-27)

(3.141592653589793, 4.71163431535992e-32)

(20.4448034666183, 20.4325827297121)

(73.83419918545908, 73.8308133759219)

(23.583143310284843, 23.5725472811462)

(26.72224637418772, 26.7128941475173)

(-306.30691607324667, -306.306099900576)

(14.172432074799941, 14.1548141232633)

(-75.39822368615503, -6.51336327755355e-28)

(-42.423286257700816, -42.4173940862181)

(58.12806557615112, 58.1237650459065)

(-7.917052684666207, -7.88560072412753)

(56.548667764616276, 2.7478251327179e-28)

(51.84592244522343, 51.8411009136761)

(-17.307640537414635, -17.2932080946897)

(-14.172432074799941, -14.1548141232633)

(15.707963267948966, 5.8895428941999e-30)

(45.56406659619972, 45.5585804770373)

(1.8365972031521258, 1.70986852923209)

(89.54097460498406, 89.5381826741839)

(7.917052684666207, 7.88560072412753)

(-73.83419918545908, -73.8308133759219)

(-59.69026041820607, -8.97021321364436e-29)

(21.991148575128552, 1.61609057016845e-29)

(6.283185307179586, 3.76930745228793e-31)

(-87.96459430051421, -1.03429796490781e-27)

(-28.274333882308138, -3.43478141589738e-29)

(-67.5516436614121, -67.5479429919577)

(-9.42477796076938, -1.27214126514718e-30)

(42.423286257700816, 42.4173940862181)

(59.69026041820607, 8.97021321364436e-29)

(-83.25821066164869, -83.255208063081)

(28.274333882308138, 3.43478141589738e-29)

(94.2477796076938, 1.10977728956951e-27)

(-29.861872403816044, -29.853502870657)

(-72.25663103256524, -2.93139900017185e-27)

(-84.82300164692441, -3.99087542625273e-27)

(70.692907433161, 70.6893711873986)

(-105.24810453889911, -105.245729252817)

(-51.84592244522343, -51.8411009136761)

(-4.815842317845935, -4.76448393290203)

(-97.3893722612836, -4.58542475390885e-27)

(37.69911184307752, 8.14170409694193e-29)

(-50.26548245743669, -1.92988541557142e-28)

(-94.2477796076938, -1.10977728956951e-27)

(36.142148897006074, 36.135233089007)

(-37.69911184307752, -8.14170409694193e-29)

(-61.269217268722585, -61.2651371880071)

(-64.41041196277601, -64.4065308365988)

(-95.82379379784489, -95.8211849135206)

(-23.583143310284843, -23.5725472811462)

(-20.4448034666183, -20.4325827297121)

(-58.12806557615112, -58.1237650459065)

(-81.68140899333463, -1.25601110053315e-27)

(43.982297150257104, 1.29287245613476e-28)

(48.70495166667517, 48.6998192592491)

(-1.8365972031521258, -1.70986852923209)

(-36.142148897006074, -36.135233089007)

(-31.41592653589793, -4.71163431535992e-29)

(0, 0)

(-39.282635752723394, -39.2762726485285)

(-21.991148575128552, -1.61609057016845e-29)

(100.53096491487338, 1.54390833245714e-27)

(34.55751918948773, 1.68111309202325e-28)

(278.0327481900649, 278.031849018319)

(65.97344572538566, 6.34844983898999e-29)

(92.68237799735202, 92.6796806914592)

(-45.56406659619972, -45.5585804770373)

(80.11685346965491, 80.1137331491182)

(-53.40707511102649, -1.15535214562331e-28)

(-89.54097460498406, -89.5381826741839)

(95.82379379784489, 95.8211849135206)

(-6.283185307179586, -3.76930745228793e-31)

(25.132741228718345, 2.41235676946428e-29)

(64.41041196277601, 64.4065308365988)

(-43.982297150257104, -1.29287245613476e-28)

(72.25663103256524, 2.93139900017185e-27)

(-80.11685346965491, -80.1137331491182)

(29.861872403816044, 29.853502870657)

(87.96459430051421, 1.03429796490781e-27)


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=12.5663706143592x_{1} = 12.5663706143592
x2=78.5398163397448x_{2} = 78.5398163397448
x3=−86.3995849739529x_{3} = -86.3995849739529
x4=50.2654824574367x_{4} = 50.2654824574367
x5=81.6814089933346x_{5} = 81.6814089933346
x6=3.14159265358979x_{6} = 3.14159265358979
x7=−306.306916073247x_{7} = -306.306916073247
x8=−42.4232862577008x_{8} = -42.4232862577008
x9=−7.91705268466621x_{9} = -7.91705268466621
x10=56.5486677646163x_{10} = 56.5486677646163
x11=−17.3076405374146x_{11} = -17.3076405374146
x12=−14.1724320747999x_{12} = -14.1724320747999
x13=15.707963267949x_{13} = 15.707963267949
x14=−73.8341991854591x_{14} = -73.8341991854591
x15=21.9911485751286x_{15} = 21.9911485751286
x16=6.28318530717959x_{16} = 6.28318530717959
x17=−67.5516436614121x_{17} = -67.5516436614121
x18=59.6902604182061x_{18} = 59.6902604182061
x19=−83.2582106616487x_{19} = -83.2582106616487
x20=28.2743338823081x_{20} = 28.2743338823081
x21=94.2477796076938x_{21} = 94.2477796076938
x22=−29.861872403816x_{22} = -29.861872403816
x23=−105.248104538899x_{23} = -105.248104538899
x24=−51.8459224452234x_{24} = -51.8459224452234
x25=−4.81584231784594x_{25} = -4.81584231784594
x26=37.6991118430775x_{26} = 37.6991118430775
x27=−61.2692172687226x_{27} = -61.2692172687226
x28=−64.410411962776x_{28} = -64.410411962776
x29=−95.8237937978449x_{29} = -95.8237937978449
x30=−23.5831433102848x_{30} = -23.5831433102848
x31=−20.4448034666183x_{31} = -20.4448034666183
x32=−58.1280655761511x_{32} = -58.1280655761511
x33=43.9822971502571x_{33} = 43.9822971502571
x34=−1.83659720315213x_{34} = -1.83659720315213
x35=−36.1421488970061x_{35} = -36.1421488970061
x36=−39.2826357527234x_{36} = -39.2826357527234
x37=100.530964914873x_{37} = 100.530964914873
x38=34.5575191894877x_{38} = 34.5575191894877
x39=65.9734457253857x_{39} = 65.9734457253857
x40=−45.5640665961997x_{40} = -45.5640665961997
x41=−89.5409746049841x_{41} = -89.5409746049841
x42=25.1327412287183x_{42} = 25.1327412287183
x43=72.2566310325652x_{43} = 72.2566310325652
x44=−80.1168534696549x_{44} = -80.1168534696549
x45=87.9645943005142x_{45} = 87.9645943005142
Maxima of the function at points:
x45=67.5516436614121x_{45} = 67.5516436614121
x45=86.3995849739529x_{45} = 86.3995849739529
x45=−65.9734457253857x_{45} = -65.9734457253857
x45=−15.707963267949x_{45} = -15.707963267949
x45=20.4448034666183x_{45} = 20.4448034666183
x45=73.8341991854591x_{45} = 73.8341991854591
x45=23.5831433102848x_{45} = 23.5831433102848
x45=26.7222463741877x_{45} = 26.7222463741877
x45=14.1724320747999x_{45} = 14.1724320747999
x45=−75.398223686155x_{45} = -75.398223686155
x45=58.1280655761511x_{45} = 58.1280655761511
x45=51.8459224452234x_{45} = 51.8459224452234
x45=45.5640665961997x_{45} = 45.5640665961997
x45=1.83659720315213x_{45} = 1.83659720315213
x45=89.5409746049841x_{45} = 89.5409746049841
x45=7.91705268466621x_{45} = 7.91705268466621
x45=−59.6902604182061x_{45} = -59.6902604182061
x45=−87.9645943005142x_{45} = -87.9645943005142
x45=−28.2743338823081x_{45} = -28.2743338823081
x45=−9.42477796076938x_{45} = -9.42477796076938
x45=42.4232862577008x_{45} = 42.4232862577008
x45=−72.2566310325652x_{45} = -72.2566310325652
x45=−84.8230016469244x_{45} = -84.8230016469244
x45=70.692907433161x_{45} = 70.692907433161
x45=−97.3893722612836x_{45} = -97.3893722612836
x45=−50.2654824574367x_{45} = -50.2654824574367
x45=−94.2477796076938x_{45} = -94.2477796076938
x45=36.1421488970061x_{45} = 36.1421488970061
x45=−37.6991118430775x_{45} = -37.6991118430775
x45=−81.6814089933346x_{45} = -81.6814089933346
x45=48.7049516666752x_{45} = 48.7049516666752
x45=−31.4159265358979x_{45} = -31.4159265358979
x45=−21.9911485751286x_{45} = -21.9911485751286
x45=278.032748190065x_{45} = 278.032748190065
x45=92.682377997352x_{45} = 92.682377997352
x45=80.1168534696549x_{45} = 80.1168534696549
x45=−53.4070751110265x_{45} = -53.4070751110265
x45=95.8237937978449x_{45} = 95.8237937978449
x45=−6.28318530717959x_{45} = -6.28318530717959
x45=64.410411962776x_{45} = 64.410411962776
x45=−43.9822971502571x_{45} = -43.9822971502571
x45=29.861872403816x_{45} = 29.861872403816
Decreasing at intervals
[100.530964914873,∞)\left[100.530964914873, \infty\right)
Increasing at intervals
(−∞,−306.306916073247]\left(-\infty, -306.306916073247\right]
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
2(−x(sin⁡2(x)−cos⁡2(x))+2sin⁡(x)cos⁡(x))=02 \left(- x \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) = 0
Solve this equation
The roots of this equation
x1=−77.760847792972x_{1} = -77.760847792972
x2=71.4782275499213x_{2} = 71.4782275499213
x3=99.7505790857949x_{3} = 99.7505790857949
x4=30.6468374831214x_{4} = 30.6468374831214
x5=46.3492776216985x_{5} = 46.3492776216985
x6=−46.3492776216985x_{6} = -46.3492776216985
x7=41.6381085824888x_{7} = 41.6381085824888
x8=−10.2587614549708x_{8} = -10.2587614549708
x9=52.6311758774383x_{9} = 52.6311758774383
x10=−35.3570550332742x_{10} = -35.3570550332742
x11=38.4974949445838x_{11} = 38.4974949445838
x12=−27.5071048394191x_{12} = -27.5071048394191
x13=−91.8970257752571x_{13} = -91.8970257752571
x14=−21.2292853858495x_{14} = -21.2292853858495
x15=5.58635293416499x_{15} = 5.58635293416499
x16=−63.6251091208926x_{16} = -63.6251091208926
x17=−32.2168395518658x_{17} = -32.2168395518658
x18=−76.1901839979235x_{18} = -76.1901839979235
x19=−79.3315168346756x_{19} = -79.3315168346756
x20=−60.4839244878466x_{20} = -60.4839244878466
x21=−40.0677825970372x_{21} = -40.0677825970372
x22=0x_{22} = 0
x23=91.8970257752571x_{23} = 91.8970257752571
x24=−47.9197205706165x_{24} = -47.9197205706165
x25=76.1901839979235x_{25} = 76.1901839979235
x26=47.9197205706165x_{26} = 47.9197205706165
x27=66.766332133246x_{27} = 66.766332133246
x28=−90.3263240494369x_{28} = -90.3263240494369
x29=69.9075883539626x_{29} = 69.9075883539626
x30=−13.3890435377793x_{30} = -13.3890435377793
x31=−82.4728694594266x_{31} = -82.4728694594266
x32=8.69662198229738x_{32} = 8.69662198229738
x33=32.2168395518658x_{33} = 32.2168395518658
x34=88.7556256712795x_{34} = 88.7556256712795
x35=−58.9133484807877x_{35} = -58.9133484807877
x36=33.7869153354295x_{36} = 33.7869153354295
x37=−18.0917665453763x_{37} = -18.0917665453763
x38=120.170079673253x_{38} = 120.170079673253
x39=−24.3678503974527x_{39} = -24.3678503974527
x40=−62.0545116429054x_{40} = -62.0545116429054
x41=74.6195257807054x_{41} = 74.6195257807054
x42=4.04808180161146x_{42} = 4.04808180161146
x43=−84.0435524991391x_{43} = -84.0435524991391
x44=19.6603640661261x_{44} = 19.6603640661261
x45=98.1798629425939x_{45} = 98.1798629425939
x46=54.2016970313842x_{46} = 54.2016970313842
x47=68.3369563786298x_{47} = 68.3369563786298
x48=−66.766332133246x_{48} = -66.766332133246
x49=27.5071048394191x_{49} = 27.5071048394191
x50=−19.6603640661261x_{50} = -19.6603640661261
x51=63.6251091208926x_{51} = 63.6251091208926
x52=−99.7505790857949x_{52} = -99.7505790857949
x53=2.54349254705114x_{53} = 2.54349254705114
x54=−41.6381085824888x_{54} = -41.6381085824888
x55=−1.1444648640517x_{55} = -1.1444648640517
x56=−49.4901859325761x_{56} = -49.4901859325761
x57=−4.04808180161146x_{57} = -4.04808180161146
x58=25.9374070267134x_{58} = 25.9374070267134
x59=−68.3369563786298x_{59} = -68.3369563786298
x60=90.3263240494369x_{60} = 90.3263240494369
x61=85.6142396947314x_{61} = 85.6142396947314
x62=−85.6142396947314x_{62} = -85.6142396947314
x63=82.4728694594266x_{63} = 82.4728694594266
x64=−93.4677306800165x_{64} = -93.4677306800165
x65=96.6091494063022x_{65} = 96.6091494063022
x66=55.7722336752062x_{66} = 55.7722336752062
x67=−54.2016970313842x_{67} = -54.2016970313842
x68=11.8231619098018x_{68} = 11.8231619098018
x69=84.0435524991391x_{69} = 84.0435524991391
x70=40.0677825970372x_{70} = 40.0677825970372
x71=−98.1798629425939x_{71} = -98.1798629425939
x72=24.3678503974527x_{72} = 24.3678503974527
x73=−25.9374070267134x_{73} = -25.9374070267134
x74=18.0917665453763x_{74} = 18.0917665453763
x75=49.4901859325761x_{75} = 49.4901859325761
x76=−57.3427845371101x_{76} = -57.3427845371101
x77=62.0545116429054x_{77} = 62.0545116429054
x78=−33.7869153354295x_{78} = -33.7869153354295
x79=−11.8231619098018x_{79} = -11.8231619098018
x80=−69.9075883539626x_{80} = -69.9075883539626
x81=77.760847792972x_{81} = 77.760847792972
x82=−38.4974949445838x_{82} = -38.4974949445838
x83=10.2587614549708x_{83} = 10.2587614549708
x84=−71.4782275499213x_{84} = -71.4782275499213
x85=60.4839244878466x_{85} = 60.4839244878466
x86=−55.7722336752062x_{86} = -55.7722336752062
x87=16.5235843473527x_{87} = 16.5235843473527
x88=−5.58635293416499x_{88} = -5.58635293416499

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
[99.7505790857949,∞)\left[99.7505790857949, \infty\right)
Convex at the intervals
(−∞,−99.7505790857949]\left(-\infty, -99.7505790857949\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(xsin⁡2(x))=⟨−∞,0⟩\lim_{x \to -\infty}\left(x \sin^{2}{\left(x \right)}\right) = \left\langle -\infty, 0\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−∞,0⟩y = \left\langle -\infty, 0\right\rangle
lim⁡x→∞(xsin⁡2(x))=⟨0,∞⟩\lim_{x \to \infty}\left(x \sin^{2}{\left(x \right)}\right) = \left\langle 0, \infty\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨0,∞⟩y = \left\langle 0, \infty\right\rangle
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x*sin(x)^2, divided by x at x->+oo and x ->-oo
lim⁡x→−∞sin⁡2(x)=⟨0,1⟩\lim_{x \to -\infty} \sin^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
Let's take the limit
so,
inclined asymptote equation on the left:
y=⟨0,1⟩xy = \left\langle 0, 1\right\rangle x
lim⁡x→∞sin⁡2(x)=⟨0,1⟩\lim_{x \to \infty} \sin^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
Let's take the limit
so,
inclined asymptote equation on the right:
y=⟨0,1⟩xy = \left\langle 0, 1\right\rangle x
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:
xsin⁡2(x)=−xsin⁡2(x)x \sin^{2}{\left(x \right)} = - x \sin^{2}{\left(x \right)}
- No
xsin⁡2(x)=xsin⁡2(x)x \sin^{2}{\left(x \right)} = x \sin^{2}{\left(x \right)}
- Yes
so, the function
is
odd
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