Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • x+(lnx)/x
  • x*cbrt((x-1)^2)
  • x^-6
  • -x+5

  • Identical expressions

  • (one /2cos)(x/ three)
  • (1 divide by 2 co sinus of e of )(x divide by 3)
  • (one divide by 2 co sinus of e of )(x divide by three)
  • 1/2cosx/3
  • (1 divide by 2cos)(x divide by 3)

  • Similar expressions

  • y=1/2cosx/3
Plotting a function graph/ (1/2cos)(x/3)

Graphing y = (1/2cos)(x/3)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       cos(x) x
f(x) = ------*-
         2    3
f(x)=x3cos⁡(x)2f{\left(x \right)} = \frac{x}{3} \frac{\cos{\left(x \right)}}{2} 
f = (x/3)*(cos(x)/2)
The graph of the function
02468-8-6-4-2-10105-5
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:
x3cos⁡(x)2=0\frac{x}{3} \frac{\cos{\left(x \right)}}{2} = 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=48.6946861306418x_{1} = 48.6946861306418
x2=54.9778714378214x_{2} = 54.9778714378214
x3=−98.9601685880785x_{3} = -98.9601685880785
x4=67.5442420521806x_{4} = 67.5442420521806
x5=76.9690200129499x_{5} = 76.9690200129499
x6=36.1283155162826x_{6} = 36.1283155162826
x7=58.1194640914112x_{7} = 58.1194640914112
x8=14.1371669411541x_{8} = 14.1371669411541
x9=−29.845130209103x_{9} = -29.845130209103
x10=61.261056745001x_{10} = 61.261056745001
x11=−36.1283155162826x_{11} = -36.1283155162826
x12=−4.71238898038469x_{12} = -4.71238898038469
x13=−39.2699081698724x_{13} = -39.2699081698724
x14=1.5707963267949x_{14} = 1.5707963267949
x15=−14.1371669411541x_{15} = -14.1371669411541
x16=−64.4026493985908x_{16} = -64.4026493985908
x17=−67.5442420521806x_{17} = -67.5442420521806
x18=92.6769832808989x_{18} = 92.6769832808989
x19=−51.8362787842316x_{19} = -51.8362787842316
x20=−86.3937979737193x_{20} = -86.3937979737193
x21=42.4115008234622x_{21} = 42.4115008234622
x22=−17.2787595947439x_{22} = -17.2787595947439
x23=−45.553093477052x_{23} = -45.553093477052
x24=−89.5353906273091x_{24} = -89.5353906273091
x25=−1.5707963267949x_{25} = -1.5707963267949
x26=39.2699081698724x_{26} = 39.2699081698724
x27=23.5619449019235x_{27} = 23.5619449019235
x28=7.85398163397448x_{28} = 7.85398163397448
x29=−114.668131856027x_{29} = -114.668131856027
x30=−58.1194640914112x_{30} = -58.1194640914112
x31=−61.261056745001x_{31} = -61.261056745001
x32=−73.8274273593601x_{32} = -73.8274273593601
x33=73.8274273593601x_{33} = 73.8274273593601
x34=29.845130209103x_{34} = 29.845130209103
x35=4.71238898038469x_{35} = 4.71238898038469
x36=0x_{36} = 0
x37=86.3937979737193x_{37} = 86.3937979737193
x38=64.4026493985908x_{38} = 64.4026493985908
x39=89.5353906273091x_{39} = 89.5353906273091
x40=−20.4203522483337x_{40} = -20.4203522483337
x41=−26.7035375555132x_{41} = -26.7035375555132
x42=98.9601685880785x_{42} = 98.9601685880785
x43=51.8362787842316x_{43} = 51.8362787842316
x44=83.2522053201295x_{44} = 83.2522053201295
x45=−48.6946861306418x_{45} = -48.6946861306418
x46=−54.9778714378214x_{46} = -54.9778714378214
x47=70.6858347057703x_{47} = 70.6858347057703
x48=−95.8185759344887x_{48} = -95.8185759344887
x49=26.7035375555132x_{49} = 26.7035375555132
x50=80.1106126665397x_{50} = 80.1106126665397
x51=114.668131856027x_{51} = 114.668131856027
x52=−23.5619449019235x_{52} = -23.5619449019235
x53=−7.85398163397448x_{53} = -7.85398163397448
x54=−83.2522053201295x_{54} = -83.2522053201295
x55=−76.9690200129499x_{55} = -76.9690200129499
x56=−42.4115008234622x_{56} = -42.4115008234622
x57=−32.9867228626928x_{57} = -32.9867228626928
x58=17.2787595947439x_{58} = 17.2787595947439
x59=32.9867228626928x_{59} = 32.9867228626928
x60=20.4203522483337x_{60} = 20.4203522483337
x61=−70.6858347057703x_{61} = -70.6858347057703
x62=−10.9955742875643x_{62} = -10.9955742875643
x63=−92.6769832808989x_{63} = -92.6769832808989
x64=45.553093477052x_{64} = 45.553093477052
x65=10.9955742875643x_{65} = 10.9955742875643
x66=−80.1106126665397x_{66} = -80.1106126665397
x67=95.8185759344887x_{67} = 95.8185759344887
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (cos(x)/2)*(x/3).
03cos⁡(0)2\frac{0}{3} \frac{\cos{\left(0 \right)}}{2}
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
−xsin⁡(x)6+cos⁡(x)6=0- \frac{x \sin{\left(x \right)}}{6} + \frac{\cos{\left(x \right)}}{6} = 0
Solve this equation
The roots of this equation
x1=53.4257904773947x_{1} = 53.4257904773947
x2=−0.86033358901938x_{2} = -0.86033358901938
x3=−84.8347887180423x_{3} = -84.8347887180423
x4=−75.4114834888481x_{4} = -75.4114834888481
x5=56.5663442798215x_{5} = 56.5663442798215
x6=−40.8651703304881x_{6} = -40.8651703304881
x7=34.5864242152889x_{7} = 34.5864242152889
x8=−44.0050179208308x_{8} = -44.0050179208308
x9=−53.4257904773947x_{9} = -53.4257904773947
x10=−12.6452872238566x_{10} = -12.6452872238566
x11=−78.5525459842429x_{11} = -78.5525459842429
x12=75.4114834888481x_{12} = 75.4114834888481
x13=47.145097736761x_{13} = 47.145097736761
x14=−3.42561845948173x_{14} = -3.42561845948173
x15=−100.540910786842x_{15} = -100.540910786842
x16=−147.661626855354x_{16} = -147.661626855354
x17=97.3996388790738x_{17} = 97.3996388790738
x18=−94.2583883450399x_{18} = -94.2583883450399
x19=−15.7712848748159x_{19} = -15.7712848748159
x20=87.9759605524932x_{20} = 87.9759605524932
x21=91.1171613944647x_{21} = 91.1171613944647
x22=−69.1295029738953x_{22} = -69.1295029738953
x23=15.7712848748159x_{23} = 15.7712848748159
x24=69.1295029738953x_{24} = 69.1295029738953
x25=−31.4477146375462x_{25} = -31.4477146375462
x26=−18.90240995686x_{26} = -18.90240995686
x27=22.0364967279386x_{27} = 22.0364967279386
x28=18.90240995686x_{28} = 18.90240995686
x29=−72.270467060309x_{29} = -72.270467060309
x30=−22.0364967279386x_{30} = -22.0364967279386
x31=−9.52933440536196x_{31} = -9.52933440536196
x32=28.309642854452x_{32} = 28.309642854452
x33=81.6936492356017x_{33} = 81.6936492356017
x34=−47.145097736761x_{34} = -47.145097736761
x35=25.1724463266467x_{35} = 25.1724463266467
x36=3.42561845948173x_{36} = 3.42561845948173
x37=78.5525459842429x_{37} = 78.5525459842429
x38=37.7256128277765x_{38} = 37.7256128277765
x39=−81.6936492356017x_{39} = -81.6936492356017
x40=100.540910786842x_{40} = 100.540910786842
x41=62.8477631944545x_{41} = 62.8477631944545
x42=−91.1171613944647x_{42} = -91.1171613944647
x43=31.4477146375462x_{43} = 31.4477146375462
x44=−97.3996388790738x_{44} = -97.3996388790738
x45=−65.9885986984904x_{45} = -65.9885986984904
x46=40.8651703304881x_{46} = 40.8651703304881
x47=65.9885986984904x_{47} = 65.9885986984904
x48=−56.5663442798215x_{48} = -56.5663442798215
x49=−116.247530303932x_{49} = -116.247530303932
x50=−59.7070073053355x_{50} = -59.7070073053355
x51=−34.5864242152889x_{51} = -34.5864242152889
x52=50.2853663377737x_{52} = 50.2853663377737
x53=94.2583883450399x_{53} = 94.2583883450399
x54=−25.1724463266467x_{54} = -25.1724463266467
x55=−6.43729817917195x_{55} = -6.43729817917195
x56=−62.8477631944545x_{56} = -62.8477631944545
x57=9.52933440536196x_{57} = 9.52933440536196
x58=−37.7256128277765x_{58} = -37.7256128277765
x59=6.43729817917195x_{59} = 6.43729817917195
x60=84.8347887180423x_{60} = 84.8347887180423
x61=−50.2853663377737x_{61} = -50.2853663377737
x62=72.270467060309x_{62} = 72.270467060309
x63=59.7070073053355x_{63} = 59.7070073053355
x64=−28.309642854452x_{64} = -28.309642854452
x65=0.86033358901938x_{65} = 0.86033358901938
x66=−87.9759605524932x_{66} = -87.9759605524932
x67=44.0050179208308x_{67} = 44.0050179208308
x68=12.6452872238566x_{68} = 12.6452872238566
The values of the extrema at the points:
(53.42579047739466, -8.90273902664936)

(-0.8603335890193797, -0.0935160563651742)

(-84.83478871804229, 14.1381492539428)

(-75.41148348884815, -12.567475678867)

(56.56634427982152, 9.42625119547937)

(-40.86517033048807, 6.8088234107529)

(34.58642421528892, -5.76199612226474)

(-44.005017920830845, -7.33227666318441)

(-53.42579047739466, 8.90273902664936)

(-12.645287223856643, -2.10098854964878)

(-78.55254598424293, 13.091030265289)

(75.41148348884815, 12.567475678867)

(47.14509773676103, -7.85574929292366)

(-3.4256184594817283, 0.548061899265149)

(-100.54091078684232, -16.755989675971)

(-147.66162685535437, 24.6097068086237)

(97.39963887907376, -16.2324176326039)

(-94.25838834503986, -15.7088473708514)

(-15.771284874815882, 2.62327949368896)

(87.97596055249322, 14.6617129554041)

(91.11716139446474, -15.1852790749412)

(-69.12950297389526, -11.5203785511536)

(15.771284874815882, -2.62327949368896)

(69.12950297389526, 11.5203785511536)

(-31.447714637546234, -5.23863787975577)

(-18.902409956860023, -3.14600228299484)

(22.036496727938566, -3.66897367985974)

(18.902409956860023, 3.14600228299484)

(-72.27046706030896, 12.0439249330416)

(-22.036496727938566, 3.66897367985974)

(-9.529334405361963, 1.57954904324663)

(28.30964285445201, -4.71533292318239)

(81.69364923560168, 13.6145882494208)

(-47.14509773676103, 7.85574929292366)

(25.172446326646664, 4.19210113631192)

(3.4256184594817283, -0.548061899265149)

(78.55254598424293, -13.091030265289)

(37.7256128277765, 6.28539436880166)

(-81.69364923560168, -13.6145882494208)

(100.54091078684232, 16.755989675971)

(62.84776319445445, 10.4733014953591)

(-91.11716139446474, 15.1852790749412)

(31.447714637546234, 5.23863787975577)

(-97.39963887907376, 16.2324176326039)

(-65.98859869849039, 10.9968371561319)

(40.86517033048807, -6.8088234107529)

(65.98859869849039, -10.9968371561319)

(-56.56634427982152, -9.42625119547937)

(-116.2475303039321, 19.3738715626645)

(-59.70700730533546, 9.94977247337763)

(-34.58642421528892, 5.76199612226474)

(50.28536633777365, 8.3792376725662)

(94.25838834503986, 15.7088473708514)

(-25.172446326646664, -4.19210113631192)

(-6.437298179171947, -1.06016732413898)

(-62.84776319445445, -10.4733014953591)

(9.529334405361963, -1.57954904324663)

(-37.7256128277765, -6.28539436880166)

(6.437298179171947, 1.06016732413898)

(84.83478871804229, -14.1381492539428)

(-50.28536633777365, -8.3792376725662)

(72.27046706030896, -12.0439249330416)

(59.70700730533546, -9.94977247337763)

(-28.30964285445201, 4.71533292318239)

(0.8603335890193797, 0.0935160563651742)

(-87.97596055249322, -14.6617129554041)

(44.005017920830845, 7.33227666318441)

(12.645287223856643, 2.10098854964878)


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=53.4257904773947x_{1} = 53.4257904773947
x2=−0.86033358901938x_{2} = -0.86033358901938
x3=−75.4114834888481x_{3} = -75.4114834888481
x4=34.5864242152889x_{4} = 34.5864242152889
x5=−44.0050179208308x_{5} = -44.0050179208308
x6=−12.6452872238566x_{6} = -12.6452872238566
x7=47.145097736761x_{7} = 47.145097736761
x8=−100.540910786842x_{8} = -100.540910786842
x9=97.3996388790738x_{9} = 97.3996388790738
x10=−94.2583883450399x_{10} = -94.2583883450399
x11=91.1171613944647x_{11} = 91.1171613944647
x12=−69.1295029738953x_{12} = -69.1295029738953
x13=15.7712848748159x_{13} = 15.7712848748159
x14=−31.4477146375462x_{14} = -31.4477146375462
x15=−18.90240995686x_{15} = -18.90240995686
x16=22.0364967279386x_{16} = 22.0364967279386
x17=28.309642854452x_{17} = 28.309642854452
x18=3.42561845948173x_{18} = 3.42561845948173
x19=78.5525459842429x_{19} = 78.5525459842429
x20=−81.6936492356017x_{20} = -81.6936492356017
x21=40.8651703304881x_{21} = 40.8651703304881
x22=65.9885986984904x_{22} = 65.9885986984904
x23=−56.5663442798215x_{23} = -56.5663442798215
x24=−25.1724463266467x_{24} = -25.1724463266467
x25=−6.43729817917195x_{25} = -6.43729817917195
x26=−62.8477631944545x_{26} = -62.8477631944545
x27=9.52933440536196x_{27} = 9.52933440536196
x28=−37.7256128277765x_{28} = -37.7256128277765
x29=84.8347887180423x_{29} = 84.8347887180423
x30=−50.2853663377737x_{30} = -50.2853663377737
x31=72.270467060309x_{31} = 72.270467060309
x32=59.7070073053355x_{32} = 59.7070073053355
x33=−87.9759605524932x_{33} = -87.9759605524932
Maxima of the function at points:
x33=−84.8347887180423x_{33} = -84.8347887180423
x33=56.5663442798215x_{33} = 56.5663442798215
x33=−40.8651703304881x_{33} = -40.8651703304881
x33=−53.4257904773947x_{33} = -53.4257904773947
x33=−78.5525459842429x_{33} = -78.5525459842429
x33=75.4114834888481x_{33} = 75.4114834888481
x33=−3.42561845948173x_{33} = -3.42561845948173
x33=−147.661626855354x_{33} = -147.661626855354
x33=−15.7712848748159x_{33} = -15.7712848748159
x33=87.9759605524932x_{33} = 87.9759605524932
x33=69.1295029738953x_{33} = 69.1295029738953
x33=18.90240995686x_{33} = 18.90240995686
x33=−72.270467060309x_{33} = -72.270467060309
x33=−22.0364967279386x_{33} = -22.0364967279386
x33=−9.52933440536196x_{33} = -9.52933440536196
x33=81.6936492356017x_{33} = 81.6936492356017
x33=−47.145097736761x_{33} = -47.145097736761
x33=25.1724463266467x_{33} = 25.1724463266467
x33=37.7256128277765x_{33} = 37.7256128277765
x33=100.540910786842x_{33} = 100.540910786842
x33=62.8477631944545x_{33} = 62.8477631944545
x33=−91.1171613944647x_{33} = -91.1171613944647
x33=31.4477146375462x_{33} = 31.4477146375462
x33=−97.3996388790738x_{33} = -97.3996388790738
x33=−65.9885986984904x_{33} = -65.9885986984904
x33=−116.247530303932x_{33} = -116.247530303932
x33=−59.7070073053355x_{33} = -59.7070073053355
x33=−34.5864242152889x_{33} = -34.5864242152889
x33=50.2853663377737x_{33} = 50.2853663377737
x33=94.2583883450399x_{33} = 94.2583883450399
x33=6.43729817917195x_{33} = 6.43729817917195
x33=−28.309642854452x_{33} = -28.309642854452
x33=0.86033358901938x_{33} = 0.86033358901938
x33=44.0050179208308x_{33} = 44.0050179208308
x33=12.6452872238566x_{33} = 12.6452872238566
Decreasing at intervals
[97.3996388790738,∞)\left[97.3996388790738, \infty\right)
Increasing at intervals
(−∞,−100.540910786842]\left(-\infty, -100.540910786842\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
−xcos⁡(x)+2sin⁡(x)6=0- \frac{x \cos{\left(x \right)} + 2 \sin{\left(x \right)}}{6} = 0
Solve this equation
The roots of this equation
x1=−89.5577188827244x_{1} = -89.5577188827244
x2=−73.8545010149048x_{2} = -73.8545010149048
x3=95.839441141233x_{3} = 95.839441141233
x4=58.153842078645x_{4} = 58.153842078645
x5=−20.5175229099417x_{5} = -20.5175229099417
x6=89.5577188827244x_{6} = 89.5577188827244
x7=20.5175229099417x_{7} = 20.5175229099417
x8=−26.7780870755585x_{8} = -26.7780870755585
x9=51.8748140534268x_{9} = 51.8748140534268
x10=33.0471686947054x_{10} = 33.0471686947054
x11=39.3207281322521x_{11} = 39.3207281322521
x12=17.3932439645948x_{12} = 17.3932439645948
x13=64.4336791037316x_{13} = 64.4336791037316
x14=−61.2936749662429x_{14} = -61.2936749662429
x15=−98.9803718651523x_{15} = -98.9803718651523
x16=−17.3932439645948x_{16} = -17.3932439645948
x17=−36.1835330907526x_{17} = -36.1835330907526
x18=−29.9118938695518x_{18} = -29.9118938695518
x19=26.7780870755585x_{19} = 26.7780870755585
x20=−11.17270586833x_{20} = -11.17270586833
x21=67.573830670859x_{21} = 67.573830670859
x22=92.6985552433969x_{22} = 92.6985552433969
x23=29.9118938695518x_{23} = 29.9118938695518
x24=5.08698509410227x_{24} = 5.08698509410227
x25=−8.09616360322292x_{25} = -8.09616360322292
x26=98.9803718651523x_{26} = 98.9803718651523
x27=36.1835330907526x_{27} = 36.1835330907526
x28=55.0142096788381x_{28} = 55.0142096788381
x29=−67.573830670859x_{29} = -67.573830670859
x30=76.9949898891676x_{30} = 76.9949898891676
x31=2.2889297281034x_{31} = 2.2889297281034
x32=70.7141100665485x_{32} = 70.7141100665485
x33=−5.08698509410227x_{33} = -5.08698509410227
x34=−48.7357007949054x_{34} = -48.7357007949054
x35=86.4169374541167x_{35} = 86.4169374541167
x36=−64.4336791037316x_{36} = -64.4336791037316
x37=−58.153842078645x_{37} = -58.153842078645
x38=−45.5969279840735x_{38} = -45.5969279840735
x39=11.17270586833x_{39} = 11.17270586833
x40=14.2763529183365x_{40} = 14.2763529183365
x41=−33.0471686947054x_{41} = -33.0471686947054
x42=−2.2889297281034x_{42} = -2.2889297281034
x43=−86.4169374541167x_{43} = -86.4169374541167
x44=−80.1355651940744x_{44} = -80.1355651940744
x45=61.2936749662429x_{45} = 61.2936749662429
x46=45.5969279840735x_{46} = 45.5969279840735
x47=−51.8748140534268x_{47} = -51.8748140534268
x48=80.1355651940744x_{48} = 80.1355651940744
x49=0x_{49} = 0
x50=8.09616360322292x_{50} = 8.09616360322292
x51=−42.458570771699x_{51} = -42.458570771699
x52=−55.0142096788381x_{52} = -55.0142096788381
x53=−70.7141100665485x_{53} = -70.7141100665485
x54=−76.9949898891676x_{54} = -76.9949898891676
x55=−95.839441141233x_{55} = -95.839441141233
x56=−23.6463238196036x_{56} = -23.6463238196036
x57=23.6463238196036x_{57} = 23.6463238196036
x58=−14.2763529183365x_{58} = -14.2763529183365
x59=42.458570771699x_{59} = 42.458570771699
x60=48.7357007949054x_{60} = 48.7357007949054
x61=83.2762171649775x_{61} = 83.2762171649775
x62=73.8545010149048x_{62} = 73.8545010149048
x63=−39.3207281322521x_{63} = -39.3207281322521
x64=−92.6985552433969x_{64} = -92.6985552433969
x65=−83.2762171649775x_{65} = -83.2762171649775

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
[95.839441141233,∞)\left[95.839441141233, \infty\right)
Convex at the intervals
(−∞,−95.839441141233]\left(-\infty, -95.839441141233\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(x3cos⁡(x)2)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{x}{3} \frac{\cos{\left(x \right)}}{2}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(x3cos⁡(x)2)=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{x}{3} \frac{\cos{\left(x \right)}}{2}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (cos(x)/2)*(x/3), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(cos⁡(x)6)=⟨−16,16⟩\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{6}\right) = \left\langle - \frac{1}{6}, \frac{1}{6}\right\rangle
Let's take the limit
so,
inclined asymptote equation on the left:
y=⟨−16,16⟩xy = \left\langle - \frac{1}{6}, \frac{1}{6}\right\rangle x
lim⁡x→∞(cos⁡(x)6)=⟨−16,16⟩\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{6}\right) = \left\langle - \frac{1}{6}, \frac{1}{6}\right\rangle
Let's take the limit
so,
inclined asymptote equation on the right:
y=⟨−16,16⟩xy = \left\langle - \frac{1}{6}, \frac{1}{6}\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:
x3cos⁡(x)2=−xcos⁡(x)6\frac{x}{3} \frac{\cos{\left(x \right)}}{2} = - \frac{x \cos{\left(x \right)}}{6}
- No
x3cos⁡(x)2=xcos⁡(x)6\frac{x}{3} \frac{\cos{\left(x \right)}}{2} = \frac{x \cos{\left(x \right)}}{6}
- No
so, the function
not is
neither even, nor odd
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