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Plotting a function graph/ sin(2*x)/(x-1)

Graphing y = sin(2*x)/(x-1)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       sin(2*x)
f(x) = --------
        x - 1
f(x)=sin⁡(2x)x−1f{\left(x \right)} = \frac{\sin{\left(2 x \right)}}{x - 1} 
f = sin(2*x)/(x - 1)
The graph of the function
02468-8-6-4-2-1010-5050
The domain of the function
The points at which the function is not precisely defined:
x1=1x_{1} = 1
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⁡(2x)x−1=0\frac{\sin{\left(2 x \right)}}{x - 1} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=π2x_{2} = \frac{\pi}{2}
Numerical solution
x1=65.9734457253857x_{1} = 65.9734457253857
x2=−64.4026493985908x_{2} = -64.4026493985908
x3=−23.5619449019235x_{3} = -23.5619449019235
x4=−29.845130209103x_{4} = -29.845130209103
x5=−21.9911485751286x_{5} = -21.9911485751286
x6=21.9911485751286x_{6} = 21.9911485751286
x7=155.508836352695x_{7} = 155.508836352695
x8=−15.707963267949x_{8} = -15.707963267949
x9=42.4115008234622x_{9} = 42.4115008234622
x10=4.71238898038469x_{10} = 4.71238898038469
x11=36.1283155162826x_{11} = 36.1283155162826
x12=23.5619449019235x_{12} = 23.5619449019235
x13=6.28318530717959x_{13} = 6.28318530717959
x14=−17.2787595947439x_{14} = -17.2787595947439
x15=26.7035375555132x_{15} = 26.7035375555132
x16=−80.1106126665397x_{16} = -80.1106126665397
x17=86.3937979737193x_{17} = 86.3937979737193
x18=64.4026493985908x_{18} = 64.4026493985908
x19=−83.2522053201295x_{19} = -83.2522053201295
x20=−95.8185759344887x_{20} = -95.8185759344887
x21=28.2743338823081x_{21} = 28.2743338823081
x22=−94.2477796076938x_{22} = -94.2477796076938
x23=−1.5707963267949x_{23} = -1.5707963267949
x24=−86.3937979737193x_{24} = -86.3937979737193
x25=73.8274273593601x_{25} = 73.8274273593601
x26=−53.4070751110265x_{26} = -53.4070751110265
x27=−39.2699081698724x_{27} = -39.2699081698724
x28=−380.132711084365x_{28} = -380.132711084365
x29=67.5442420521806x_{29} = 67.5442420521806
x30=70.6858347057703x_{30} = 70.6858347057703
x31=59.6902604182061x_{31} = 59.6902604182061
x32=56.5486677646163x_{32} = 56.5486677646163
x33=125.663706143592x_{33} = 125.663706143592
x34=−42.4115008234622x_{34} = -42.4115008234622
x35=72.2566310325652x_{35} = 72.2566310325652
x36=−50.2654824574367x_{36} = -50.2654824574367
x37=−51.8362787842316x_{37} = -51.8362787842316
x38=58.1194640914112x_{38} = 58.1194640914112
x39=−73.8274273593601x_{39} = -73.8274273593601
x40=51.8362787842316x_{40} = 51.8362787842316
x41=78.5398163397448x_{41} = 78.5398163397448
x42=−87.9645943005142x_{42} = -87.9645943005142
x43=37.6991118430775x_{43} = 37.6991118430775
x44=−6.28318530717959x_{44} = -6.28318530717959
x45=−37.6991118430775x_{45} = -37.6991118430775
x46=−43.9822971502571x_{46} = -43.9822971502571
x47=29.845130209103x_{47} = 29.845130209103
x48=−45.553093477052x_{48} = -45.553093477052
x49=80.1106126665397x_{49} = 80.1106126665397
x50=−58.1194640914112x_{50} = -58.1194640914112
x51=−100.530964914873x_{51} = -100.530964914873
x52=−36.1283155162826x_{52} = -36.1283155162826
x53=−72.2566310325652x_{53} = -72.2566310325652
x54=−81.6814089933346x_{54} = -81.6814089933346
x55=−65.9734457253857x_{55} = -65.9734457253857
x56=0x_{56} = 0
x57=−28.2743338823081x_{57} = -28.2743338823081
x58=−67.5442420521806x_{58} = -67.5442420521806
x59=43.9822971502571x_{59} = 43.9822971502571
x60=100.530964914873x_{60} = 100.530964914873
x61=−7.85398163397448x_{61} = -7.85398163397448
x62=48.6946861306418x_{62} = 48.6946861306418
x63=−97.3893722612836x_{63} = -97.3893722612836
x64=89.5353906273091x_{64} = 89.5353906273091
x65=81.6814089933346x_{65} = 81.6814089933346
x66=−75.398223686155x_{66} = -75.398223686155
x67=−109.955742875643x_{67} = -109.955742875643
x68=7.85398163397448x_{68} = 7.85398163397448
x69=−14.1371669411541x_{69} = -14.1371669411541
x70=50.2654824574367x_{70} = 50.2654824574367
x71=94.2477796076938x_{71} = 94.2477796076938
x72=135.088484104361x_{72} = 135.088484104361
x73=−59.6902604182061x_{73} = -59.6902604182061
x74=12.5663706143592x_{74} = 12.5663706143592
x75=−153.9380400259x_{75} = -153.9380400259
x76=14.1371669411541x_{76} = 14.1371669411541
x77=34.5575191894877x_{77} = 34.5575191894877
x78=20.4203522483337x_{78} = 20.4203522483337
x79=45.553093477052x_{79} = 45.553093477052
x80=95.8185759344887x_{80} = 95.8185759344887
x81=15.707963267949x_{81} = 15.707963267949
x82=−89.5353906273091x_{82} = -89.5353906273091
x83=87.9645943005142x_{83} = 87.9645943005142
x84=92.6769832808989x_{84} = 92.6769832808989
x85=−9.42477796076938x_{85} = -9.42477796076938
x86=−20.4203522483337x_{86} = -20.4203522483337
x87=−31.4159265358979x_{87} = -31.4159265358979
x88=−61.261056745001x_{88} = -61.261056745001
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to sin(2*x)/(x - 1).
sin⁡(0⋅2)−1\frac{\sin{\left(0 \cdot 2 \right)}}{-1}
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
2cos⁡(2x)x−1−sin⁡(2x)(x−1)2=0\frac{2 \cos{\left(2 x \right)}}{x - 1} - \frac{\sin{\left(2 x \right)}}{\left(x - 1\right)^{2}} = 0
Solve this equation
The roots of this equation
x1=−84.0346635398793x_{1} = -84.0346635398793
x2=88.7471433991491x_{2} = 88.7471433991491
x3=−76.1803827297937x_{3} = -76.1803827297937
x4=−38.478177732588x_{4} = -38.478177732588
x5=−71.4677831150521x_{5} = -71.4677831150521
x6=−85.6055131901373x_{6} = -85.6055131901373
x7=32.1933108467876x_{7} = 32.1933108467876
x8=−0.637196330969125x_{8} = -0.637196330969125
x9=−13.3343352045635x_{9} = -13.3343352045635
x10=84.0345927265613x_{10} = 84.0345927265613
x11=71.4676852032561x_{11} = 71.4676852032561
x12=98.172197695036x_{12} = 98.172197695036
x13=−33.7649303669424x_{13} = -33.7649303669424
x14=76.1802965592094x_{14} = 76.1802965592094
x15=18.0494987719381x_{15} = 18.0494987719381
x16=−62.0424894121024x_{16} = -62.0424894121024
x17=40.0489044548563x_{17} = 40.0489044548563
x18=−98.1722495795572x_{18} = -98.1722495795572
x19=−79.3221020750003x_{19} = -79.3221020750003
x20=19.6215319912886x_{20} = 19.6215319912886
x21=−82.4638118824473x_{21} = -82.4638118824473
x22=77.7511609427056x_{22} = 77.7511609427056
x23=−55.7588651168628x_{23} = -55.7588651168628
x24=−140.584505525547x_{24} = -140.584505525547
x25=−27.4801585795776x_{25} = -27.4801585795776
x26=41.6199483594113x_{26} = 41.6199483594113
x27=63.6132585554971x_{27} = 63.6132585554971
x28=47.9039581285518x_{28} = 47.9039581285518
x29=−91.8888937560759x_{29} = -91.8888937560759
x30=−46.3332101330021x_{30} = -46.3332101330021
x31=−40.049216384194x_{31} = -40.049216384194
x32=8.60656064608673x_{32} = 8.60656064608673
x33=66.7550419722411x_{33} = 66.7550419722411
x34=85.6054449521595x_{34} = 85.6054449521595
x35=−25.9088498373569x_{35} = -25.9088498373569
x36=−16.4790625040945x_{36} = -16.4790625040945
x37=74.6094292709781x_{37} = 74.6094292709781
x38=−68.3260341292281x_{38} = -68.3260341292281
x39=82.4637383451864x_{39} = 82.4637383451864
x40=90.317989831739x_{40} = 90.317989831739
x41=24.3366319328506x_{41} = 24.3366319328506
x42=−93.4597348386756x_{42} = -93.4597348386756
x43=−65.1842703012744x_{43} = -65.1842703012744
x44=69.8968079909424x_{44} = 69.8968079909424
x45=−3.87589679173726x_{45} = -3.87589679173726
x46=−57.3297800576259x_{46} = -57.3297800576259
x47=−18.0510381254578x_{47} = -18.0510381254578
x48=54.1877730844831x_{48} = 54.1877730844831
x49=−99.743085211956x_{49} = -99.743085211956
x50=30.6220895261697x_{50} = 30.6220895261697
x51=−60.4715917520353x_{51} = -60.4715917520353
x52=96.601359096144x_{52} = 96.601359096144
x53=−32.1937937404494x_{53} = -32.1937937404494
x54=55.7587042438767x_{54} = 55.7587042438767
x55=−19.6228339741551x_{55} = -19.6228339741551
x56=−35.336037565231x_{56} = -35.336037565231
x57=2.15134433588925x_{57} = 2.15134433588925
x58=62.042359483332x_{58} = 62.042359483332
x59=−90.3180511337085x_{59} = -90.3180511337085
x60=25.9081038458568x_{60} = 25.9081038458568
x61=−2.28057021563236x_{61} = -2.28057021563236
x62=44.7619828411789x_{62} = 44.7619828411789
x63=−49.4751315219363x_{63} = -49.4751315219363
x64=−77.7512436659628x_{64} = -77.7512436659628
x65=52.6168337179501x_{65} = 52.6168337179501
x66=−69.8969103540797x_{66} = -69.8969103540797
x67=−47.9041761074919x_{67} = -47.9041761074919
x68=10.1829786980484x_{68} = 10.1829786980484
x69=−41.6202371710741x_{69} = -41.6202371710741
x70=46.33297711484x_{70} = 46.33297711484
x71=16.4772142695041x_{71} = 16.4772142695041
x72=68.3259270041136x_{72} = 68.3259270041136
x73=−10.1878453044909x_{73} = -10.1878453044909
x74=22.7650624601772x_{74} = 22.7650624601772
x75=−54.1879434234347x_{75} = -54.1879434234347
x76=−5.45915944962428x_{76} = -5.45915944962428
x77=38.4778397936073x_{77} = 38.4778397936073
x78=3.83985112537054x_{78} = 3.83985112537054
x79=91.8888345323567x_{79} = 91.8888345323567
x80=−11.7613921271159x_{80} = -11.7613921271159
x81=93.4596775892801x_{81} = 93.4596775892801
x82=33.76449140679x_{82} = 33.76449140679
x83=60.471454983256x_{83} = 60.471454983256
x84=−63.6133821448946x_{84} = -63.6133821448946
x85=99.7430349489701x_{85} = 99.7430349489701
x86=−24.3374775388136x_{86} = -24.3374775388136
x87=11.7577501031099x_{87} = 11.7577501031099
The values of the extrema at the points:
(-84.03466353987932, -0.011759706828775)

(88.74714339914914, 0.0113961973799546)

(-76.18038272979369, 0.0129563884100013)

(-38.47817773258804, 0.0253284184609493)

(-71.46778311505214, -0.0137989069832578)

(-85.60551319013732, 0.0115464165970439)

(32.19331084678758, 0.0320540376107124)

(-0.637196330969125, 0.584165185611747)

(-13.33433520456351, 0.0697201640933345)

(84.03459272656133, -0.0120429550853916)

(71.46768520325605, -0.014190544578759)

(98.172197695036, 0.0102908731702446)

(-33.76493036694237, -0.0287616451426903)

(76.18029655920942, 0.0133010633202575)

(18.049498771938094, -0.0586275451496126)

(-62.04248941210236, -0.0158618188965606)

(40.048904454856334, -0.0256068139934971)

(-98.17224957955716, 0.0100833377779178)

(-79.32210207500029, 0.0124496321661373)

(19.621531991288602, 0.0536819267559723)

(-82.46381188244735, 0.0119810254787546)

(77.75116094270562, -0.0130288424129444)

(-55.758865116862815, -0.0176177095723664)

(-140.5845055255466, -0.00706287570622247)

(-27.480158579577623, -0.0351067542272663)

(41.619948359411254, 0.0246165810275241)

(63.61325855549712, 0.0159705490539322)

(47.90395812855178, 0.0213189510240566)

(-91.88889375607587, 0.0107653937165865)

(-46.33321013300211, -0.0211256369273738)

(-40.04921638419398, -0.0243591940123493)

(8.606560646086729, -0.131182360380572)

(66.75504197224114, 0.0152075196214254)

(85.6054449521595, 0.0118193638511416)

(-25.908849837356932, 0.0371560813395048)

(-16.479062504094543, 0.0571879131957477)

(74.60942927097814, -0.0135849026536422)

(-68.32603412922812, -0.0144242203517829)

(82.46373834518636, 0.0122751691140578)

(90.317989831739, -0.0111957773969401)

(24.336631932850587, -0.0428412529680419)

(-93.45973483867563, -0.010586373047711)

(-65.18427030127438, -0.0151088991415451)

(69.89680799094245, 0.0145140783224103)

(-3.8758967917372615, 0.204020590583108)

(-57.32978005762594, 0.0171432716164381)

(-18.05103812545779, -0.0524725090383133)

(54.18777308448308, 0.0188004828697393)

(-99.74308521195597, -0.0099261173294882)

(30.622089526169745, -0.0337537827722389)

(-60.47159175203532, 0.0162671389088241)

(96.60135909614404, -0.0104599592831864)

(-32.19379374044943, 0.0301226964076625)

(55.7587042438767, -0.0182611756271808)

(-19.622833974155125, 0.0484756955066268)

(-35.33603756523104, 0.0275182822767101)

(2.1513443358892483, -0.796668913740646)

(62.04235948333203, -0.0163815170913838)

(-90.31805113370845, -0.0109505732775833)

(25.908103845856804, 0.040139489885367)

(-2.2805702156323617, -0.301345089868793)

(44.76198284117895, 0.0228493928087149)

(-49.47513152193626, -0.0198107644368111)

(-77.75124366596276, -0.0126979562288175)

(52.61683371795014, -0.0193726157649153)

(-69.89691035407965, 0.0141046362542619)

(-47.90417610749193, 0.0204470828020304)

(10.182978698048352, 0.108736064581312)

(-41.620237171074066, 0.02346141784367)

(46.33297711483998, -0.0220576552494669)

(16.47721426950408, 0.0645774211200931)

(68.3259270041136, -0.014852709331234)

(-10.187845304490947, 0.0892935867062234)

(22.765062460177248, 0.0459330744456629)

(-54.18794342343466, 0.0181191560900984)

(-5.459159449624282, -0.154357125599364)

(38.47783979360729, 0.0266800600927598)

(3.8398511253705365, 0.346796963988786)

(91.8888345323567, 0.0110022850853576)

(-11.761392127115943, -0.0783012785650106)

(93.45967758928009, -0.0108153673519588)

(33.76449140678997, -0.0305172928724435)

(60.471454983255995, 0.0168141953145683)

(-63.61338214489455, 0.0154762067428617)

(99.74303494897006, -0.0101271667464578)

(-24.337477538813616, -0.0394595455509357)

(11.757750103109899, -0.0928559995735437)


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=−84.0346635398793x_{1} = -84.0346635398793
x2=−71.4677831150521x_{2} = -71.4677831150521
x3=84.0345927265613x_{3} = 84.0345927265613
x4=71.4676852032561x_{4} = 71.4676852032561
x5=−33.7649303669424x_{5} = -33.7649303669424
x6=18.0494987719381x_{6} = 18.0494987719381
x7=−62.0424894121024x_{7} = -62.0424894121024
x8=40.0489044548563x_{8} = 40.0489044548563
x9=77.7511609427056x_{9} = 77.7511609427056
x10=−55.7588651168628x_{10} = -55.7588651168628
x11=−140.584505525547x_{11} = -140.584505525547
x12=−27.4801585795776x_{12} = -27.4801585795776
x13=−46.3332101330021x_{13} = -46.3332101330021
x14=−40.049216384194x_{14} = -40.049216384194
x15=8.60656064608673x_{15} = 8.60656064608673
x16=74.6094292709781x_{16} = 74.6094292709781
x17=−68.3260341292281x_{17} = -68.3260341292281
x18=90.317989831739x_{18} = 90.317989831739
x19=24.3366319328506x_{19} = 24.3366319328506
x20=−93.4597348386756x_{20} = -93.4597348386756
x21=−65.1842703012744x_{21} = -65.1842703012744
x22=−18.0510381254578x_{22} = -18.0510381254578
x23=−99.743085211956x_{23} = -99.743085211956
x24=30.6220895261697x_{24} = 30.6220895261697
x25=96.601359096144x_{25} = 96.601359096144
x26=55.7587042438767x_{26} = 55.7587042438767
x27=2.15134433588925x_{27} = 2.15134433588925
x28=62.042359483332x_{28} = 62.042359483332
x29=−90.3180511337085x_{29} = -90.3180511337085
x30=−2.28057021563236x_{30} = -2.28057021563236
x31=−49.4751315219363x_{31} = -49.4751315219363
x32=−77.7512436659628x_{32} = -77.7512436659628
x33=52.6168337179501x_{33} = 52.6168337179501
x34=46.33297711484x_{34} = 46.33297711484
x35=68.3259270041136x_{35} = 68.3259270041136
x36=−5.45915944962428x_{36} = -5.45915944962428
x37=−11.7613921271159x_{37} = -11.7613921271159
x38=93.4596775892801x_{38} = 93.4596775892801
x39=33.76449140679x_{39} = 33.76449140679
x40=99.7430349489701x_{40} = 99.7430349489701
x41=−24.3374775388136x_{41} = -24.3374775388136
x42=11.7577501031099x_{42} = 11.7577501031099
Maxima of the function at points:
x42=88.7471433991491x_{42} = 88.7471433991491
x42=−76.1803827297937x_{42} = -76.1803827297937
x42=−38.478177732588x_{42} = -38.478177732588
x42=−85.6055131901373x_{42} = -85.6055131901373
x42=32.1933108467876x_{42} = 32.1933108467876
x42=−0.637196330969125x_{42} = -0.637196330969125
x42=−13.3343352045635x_{42} = -13.3343352045635
x42=98.172197695036x_{42} = 98.172197695036
x42=76.1802965592094x_{42} = 76.1802965592094
x42=−98.1722495795572x_{42} = -98.1722495795572
x42=−79.3221020750003x_{42} = -79.3221020750003
x42=19.6215319912886x_{42} = 19.6215319912886
x42=−82.4638118824473x_{42} = -82.4638118824473
x42=41.6199483594113x_{42} = 41.6199483594113
x42=63.6132585554971x_{42} = 63.6132585554971
x42=47.9039581285518x_{42} = 47.9039581285518
x42=−91.8888937560759x_{42} = -91.8888937560759
x42=66.7550419722411x_{42} = 66.7550419722411
x42=85.6054449521595x_{42} = 85.6054449521595
x42=−25.9088498373569x_{42} = -25.9088498373569
x42=−16.4790625040945x_{42} = -16.4790625040945
x42=82.4637383451864x_{42} = 82.4637383451864
x42=69.8968079909424x_{42} = 69.8968079909424
x42=−3.87589679173726x_{42} = -3.87589679173726
x42=−57.3297800576259x_{42} = -57.3297800576259
x42=54.1877730844831x_{42} = 54.1877730844831
x42=−60.4715917520353x_{42} = -60.4715917520353
x42=−32.1937937404494x_{42} = -32.1937937404494
x42=−19.6228339741551x_{42} = -19.6228339741551
x42=−35.336037565231x_{42} = -35.336037565231
x42=25.9081038458568x_{42} = 25.9081038458568
x42=44.7619828411789x_{42} = 44.7619828411789
x42=−69.8969103540797x_{42} = -69.8969103540797
x42=−47.9041761074919x_{42} = -47.9041761074919
x42=10.1829786980484x_{42} = 10.1829786980484
x42=−41.6202371710741x_{42} = -41.6202371710741
x42=16.4772142695041x_{42} = 16.4772142695041
x42=−10.1878453044909x_{42} = -10.1878453044909
x42=22.7650624601772x_{42} = 22.7650624601772
x42=−54.1879434234347x_{42} = -54.1879434234347
x42=38.4778397936073x_{42} = 38.4778397936073
x42=3.83985112537054x_{42} = 3.83985112537054
x42=91.8888345323567x_{42} = 91.8888345323567
x42=60.471454983256x_{42} = 60.471454983256
x42=−63.6133821448946x_{42} = -63.6133821448946
Decreasing at intervals
[99.7430349489701,∞)\left[99.7430349489701, \infty\right)
Increasing at intervals
(−∞,−140.584505525547]\left(-\infty, -140.584505525547\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(−2sin⁡(2x)−2cos⁡(2x)x−1+sin⁡(2x)(x−1)2)x−1=0\frac{2 \left(- 2 \sin{\left(2 x \right)} - \frac{2 \cos{\left(2 x \right)}}{x - 1} + \frac{\sin{\left(2 x \right)}}{\left(x - 1\right)^{2}}\right)}{x - 1} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
x1=1x_{1} = 1
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(sin⁡(2x)x−1)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{x - 1}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(sin⁡(2x)x−1)=0\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{x - 1}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=0y = 0
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of sin(2*x)/(x - 1), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(sin⁡(2x)x(x−1))=0\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{x \left(x - 1\right)}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(sin⁡(2x)x(x−1))=0\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{x \left(x - 1\right)}\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⁡(2x)x−1=−sin⁡(2x)−x−1\frac{\sin{\left(2 x \right)}}{x - 1} = - \frac{\sin{\left(2 x \right)}}{- x - 1}
- No
sin⁡(2x)x−1=sin⁡(2x)−x−1\frac{\sin{\left(2 x \right)}}{x - 1} = \frac{\sin{\left(2 x \right)}}{- x - 1}
- No
so, the function
not is
neither even, nor odd
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