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Plotting a function graph/ sin(x)/x

Graphing y = sin(x)/x

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       sin(x)
f(x) = ------
         x
f(x)=sin⁡(x)xf{\left(x \right)} = \frac{\sin{\left(x \right)}}{x} 
f = sin(x)/x
The graph of the function
02468-8-6-4-2-10102-1
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{1} = 0
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⁡(x)x=0\frac{\sin{\left(x \right)}}{x} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=πx_{1} = \pi
Numerical solution
x1=69.1150383789755x_{1} = 69.1150383789755
x2=65.9734457253857x_{2} = 65.9734457253857
x3=−91.106186954104x_{3} = -91.106186954104
x4=590.619418874881x_{4} = 590.619418874881
x5=−59.6902604182061x_{5} = -59.6902604182061
x6=−21.9911485751286x_{6} = -21.9911485751286
x7=−370.707933123596x_{7} = -370.707933123596
x8=12.5663706143592x_{8} = 12.5663706143592
x9=21.9911485751286x_{9} = 21.9911485751286
x10=−69.1150383789755x_{10} = -69.1150383789755
x11=−100.530964914873x_{11} = -100.530964914873
x12=−223.053078404875x_{12} = -223.053078404875
x13=3.14159265358979x_{13} = 3.14159265358979
x14=−3.14159265358979x_{14} = -3.14159265358979
x15=−25.1327412287183x_{15} = -25.1327412287183
x16=−15.707963267949x_{16} = -15.707963267949
x17=−53.4070751110265x_{17} = -53.4070751110265
x18=−72.2566310325652x_{18} = -72.2566310325652
x19=153.9380400259x_{19} = 153.9380400259
x20=84.8230016469244x_{20} = 84.8230016469244
x21=−81.6814089933346x_{21} = -81.6814089933346
x22=−94.2477796076938x_{22} = -94.2477796076938
x23=18.8495559215388x_{23} = 18.8495559215388
x24=−65.9734457253857x_{24} = -65.9734457253857
x25=94.2477796076938x_{25} = 94.2477796076938
x26=9.42477796076938x_{26} = 9.42477796076938
x27=−40.8407044966673x_{27} = -40.8407044966673
x28=34.5575191894877x_{28} = 34.5575191894877
x29=97.3893722612836x_{29} = 97.3893722612836
x30=53.4070751110265x_{30} = 53.4070751110265
x31=−62.8318530717959x_{31} = -62.8318530717959
x32=59.6902604182061x_{32} = 59.6902604182061
x33=−28.2743338823081x_{33} = -28.2743338823081
x34=−56.5486677646163x_{34} = -56.5486677646163
x35=91.106186954104x_{35} = 91.106186954104
x36=15.707963267949x_{36} = 15.707963267949
x37=−18.8495559215388x_{37} = -18.8495559215388
x38=6.28318530717959x_{38} = 6.28318530717959
x39=56.5486677646163x_{39} = 56.5486677646163
x40=87.9645943005142x_{40} = 87.9645943005142
x41=31.4159265358979x_{41} = 31.4159265358979
x42=25.1327412287183x_{42} = 25.1327412287183
x43=43.9822971502571x_{43} = 43.9822971502571
x44=−47.1238898038469x_{44} = -47.1238898038469
x45=72.2566310325652x_{45} = 72.2566310325652
x46=−34.5575191894877x_{46} = -34.5575191894877
x47=47.1238898038469x_{47} = 47.1238898038469
x48=−97.3893722612836x_{48} = -97.3893722612836
x49=−50.2654824574367x_{49} = -50.2654824574367
x50=100.530964914873x_{50} = 100.530964914873
x51=81.6814089933346x_{51} = 81.6814089933346
x52=−75.398223686155x_{52} = -75.398223686155
x53=40.8407044966673x_{53} = 40.8407044966673
x54=−9.42477796076938x_{54} = -9.42477796076938
x55=78.5398163397448x_{55} = 78.5398163397448
x56=−87.9645943005142x_{56} = -87.9645943005142
x57=37.6991118430775x_{57} = 37.6991118430775
x58=−78.5398163397448x_{58} = -78.5398163397448
x59=−6.28318530717959x_{59} = -6.28318530717959
x60=50.2654824574367x_{60} = 50.2654824574367
x61=−37.6991118430775x_{61} = -37.6991118430775
x62=−43.9822971502571x_{62} = -43.9822971502571
x63=−113.097335529233x_{63} = -113.097335529233
x64=28.2743338823081x_{64} = 28.2743338823081
x65=62.8318530717959x_{65} = 62.8318530717959
x66=−31.4159265358979x_{66} = -31.4159265358979
x67=−12.5663706143592x_{67} = -12.5663706143592
x68=75.398223686155x_{68} = 75.398223686155
x69=−84.8230016469244x_{69} = -84.8230016469244
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to sin(x)/x.
sin⁡(0)0\frac{\sin{\left(0 \right)}}{0}
The result:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- the solutions of the equation d'not exist
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
cos⁡(x)x−sin⁡(x)x2=0\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}} = 0
Solve this equation
The roots of this equation
x1=−10.9041216594289x_{1} = -10.9041216594289
x2=−48.6741442319544x_{2} = -48.6741442319544
x3=45.5311340139913x_{3} = 45.5311340139913
x4=−26.6660542588127x_{4} = -26.6660542588127
x5=−73.8138806006806x_{5} = -73.8138806006806
x6=−17.2207552719308x_{6} = -17.2207552719308
x7=−64.3871195905574x_{7} = -64.3871195905574
x8=14.0661939128315x_{8} = 14.0661939128315
x9=39.2444323611642x_{9} = 39.2444323611642
x10=76.9560263103312x_{10} = 76.9560263103312
x11=23.519452498689x_{11} = 23.519452498689
x12=−23.519452498689x_{12} = -23.519452498689
x13=51.8169824872797x_{13} = 51.8169824872797
x14=−394.267341680887x_{14} = -394.267341680887
x15=58.1022547544956x_{15} = 58.1022547544956
x16=54.9596782878889x_{16} = 54.9596782878889
x17=83.2401924707234x_{17} = 83.2401924707234
x18=36.1006222443756x_{18} = 36.1006222443756
x19=−67.5294347771441x_{19} = -67.5294347771441
x20=86.3822220347287x_{20} = 86.3822220347287
x21=−70.6716857116195x_{21} = -70.6716857116195
x22=−76.9560263103312x_{22} = -76.9560263103312
x23=−32.9563890398225x_{23} = -32.9563890398225
x24=26.6660542588127x_{24} = 26.6660542588127
x25=−4.49340945790906x_{25} = -4.49340945790906
x26=42.3879135681319x_{26} = 42.3879135681319
x27=−95.8081387868617x_{27} = -95.8081387868617
x28=−51.8169824872797x_{28} = -51.8169824872797
x29=67.5294347771441x_{29} = 67.5294347771441
x30=−20.3713029592876x_{30} = -20.3713029592876
x31=−92.6661922776228x_{31} = -92.6661922776228
x32=−86.3822220347287x_{32} = -86.3822220347287
x33=−89.5242209304172x_{33} = -89.5242209304172
x34=10.9041216594289x_{34} = 10.9041216594289
x35=−98.9500628243319x_{35} = -98.9500628243319
x36=17.2207552719308x_{36} = 17.2207552719308
x37=−4355.81798462425x_{37} = -4355.81798462425
x38=32.9563890398225x_{38} = 32.9563890398225
x39=−45.5311340139913x_{39} = -45.5311340139913
x40=−54.9596782878889x_{40} = -54.9596782878889
x41=−80.0981286289451x_{41} = -80.0981286289451
x42=80.0981286289451x_{42} = 80.0981286289451
x43=−36.1006222443756x_{43} = -36.1006222443756
x44=−14.0661939128315x_{44} = -14.0661939128315
x45=−83.2401924707234x_{45} = -83.2401924707234
x46=95.8081387868617x_{46} = 95.8081387868617
x47=73.8138806006806x_{47} = 73.8138806006806
x48=−39.2444323611642x_{48} = -39.2444323611642
x49=−58.1022547544956x_{49} = -58.1022547544956
x50=−42.3879135681319x_{50} = -42.3879135681319
x51=−61.2447302603744x_{51} = -61.2447302603744
x52=108.375719651675x_{52} = 108.375719651675
x53=92.6661922776228x_{53} = 92.6661922776228
x54=4.49340945790906x_{54} = 4.49340945790906
x55=61.2447302603744x_{55} = 61.2447302603744
x56=48.6741442319544x_{56} = 48.6741442319544
x57=98.9500628243319x_{57} = 98.9500628243319
x58=−29.811598790893x_{58} = -29.811598790893
x59=20.3713029592876x_{59} = 20.3713029592876
x60=89.5242209304172x_{60} = 89.5242209304172
x61=29.811598790893x_{61} = 29.811598790893
x62=70.6716857116195x_{62} = 70.6716857116195
x63=−7.72525183693771x_{63} = -7.72525183693771
x64=7.72525183693771x_{64} = 7.72525183693771
x65=64.3871195905574x_{65} = 64.3871195905574
The values of the extrema at the points:
(-10.904121659428899, -0.0913252028230577)

(-48.674144231954386, -0.0205404540417537)

(45.53113401399128, 0.0219576982284824)

(-26.666054258812675, 0.0374745199939312)

(-73.81388060068065, -0.01354634434514)

(-17.22075527193077, -0.0579718023461539)

(-64.38711959055742, 0.0155291838074613)

(14.066193912831473, 0.0709134594504622)

(39.24443236116419, 0.0254730530928808)

(76.95602631033118, 0.0129933369870427)

(23.519452498689006, -0.0424796169776126)

(-23.519452498689006, -0.0424796169776126)

(51.81698248727967, 0.019295099487588)

(-394.26734168088706, -0.00253634191261283)

(58.10225475449559, 0.0172084874716279)

(54.959678287888934, -0.0181921463218031)

(83.2401924707234, 0.0120125604820527)

(36.10062224437561, -0.0276897323011492)

(-67.52943477714412, -0.0148067339465492)

(86.38222203472871, -0.0115756804584678)

(-70.6716857116195, 0.0141485220648664)

(-76.95602631033118, 0.0129933369870427)

(-32.956389039822476, 0.0303291711863103)

(26.666054258812675, 0.0374745199939312)

(-4.493409457909064, -0.217233628211222)

(42.38791356813192, -0.0235850682290164)

(-95.8081387868617, 0.0104369581345658)

(-51.81698248727967, 0.019295099487588)

(67.52943477714412, -0.0148067339465492)

(-20.37130295928756, 0.0490296240140742)

(-92.66619227762284, -0.0107907938495342)

(-86.38222203472871, -0.0115756804584678)

(-89.52422093041719, 0.0111694646341736)

(10.904121659428899, -0.0913252028230577)

(-98.95006282433188, -0.010105591736504)

(17.22075527193077, -0.0579718023461539)

(-4355.817984624248, 0.000229577998248987)

(32.956389039822476, 0.0303291711863103)

(-45.53113401399128, 0.0219576982284824)

(-54.959678287888934, -0.0181921463218031)

(-80.09812862894512, -0.012483713321779)

(80.09812862894512, -0.012483713321779)

(-36.10062224437561, -0.0276897323011492)

(-14.066193912831473, 0.0709134594504622)

(-83.2401924707234, 0.0120125604820527)

(95.8081387868617, 0.0104369581345658)

(73.81388060068065, -0.01354634434514)

(-39.24443236116419, 0.0254730530928808)

(-58.10225475449559, 0.0172084874716279)

(-42.38791356813192, -0.0235850682290164)

(-61.2447302603744, -0.0163257593209978)

(108.37571965167469, 0.00922676625078197)

(92.66619227762284, -0.0107907938495342)

(4.493409457909064, -0.217233628211222)

(61.2447302603744, -0.0163257593209978)

(48.674144231954386, -0.0205404540417537)

(98.95006282433188, -0.010105591736504)

(-29.81159879089296, -0.0335251350213988)

(20.37130295928756, 0.0490296240140742)

(89.52422093041719, 0.0111694646341736)

(29.81159879089296, -0.0335251350213988)

(70.6716857116195, 0.0141485220648664)

(-7.725251836937707, 0.128374553525899)

(7.725251836937707, 0.128374553525899)

(64.38711959055742, 0.0155291838074613)


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=−10.9041216594289x_{1} = -10.9041216594289
x2=−48.6741442319544x_{2} = -48.6741442319544
x3=−73.8138806006806x_{3} = -73.8138806006806
x4=−17.2207552719308x_{4} = -17.2207552719308
x5=23.519452498689x_{5} = 23.519452498689
x6=−23.519452498689x_{6} = -23.519452498689
x7=−394.267341680887x_{7} = -394.267341680887
x8=54.9596782878889x_{8} = 54.9596782878889
x9=36.1006222443756x_{9} = 36.1006222443756
x10=−67.5294347771441x_{10} = -67.5294347771441
x11=86.3822220347287x_{11} = 86.3822220347287
x12=−4.49340945790906x_{12} = -4.49340945790906
x13=42.3879135681319x_{13} = 42.3879135681319
x14=67.5294347771441x_{14} = 67.5294347771441
x15=−92.6661922776228x_{15} = -92.6661922776228
x16=−86.3822220347287x_{16} = -86.3822220347287
x17=10.9041216594289x_{17} = 10.9041216594289
x18=−98.9500628243319x_{18} = -98.9500628243319
x19=17.2207552719308x_{19} = 17.2207552719308
x20=−54.9596782878889x_{20} = -54.9596782878889
x21=−80.0981286289451x_{21} = -80.0981286289451
x22=80.0981286289451x_{22} = 80.0981286289451
x23=−36.1006222443756x_{23} = -36.1006222443756
x24=73.8138806006806x_{24} = 73.8138806006806
x25=−42.3879135681319x_{25} = -42.3879135681319
x26=−61.2447302603744x_{26} = -61.2447302603744
x27=92.6661922776228x_{27} = 92.6661922776228
x28=4.49340945790906x_{28} = 4.49340945790906
x29=61.2447302603744x_{29} = 61.2447302603744
x30=48.6741442319544x_{30} = 48.6741442319544
x31=98.9500628243319x_{31} = 98.9500628243319
x32=−29.811598790893x_{32} = -29.811598790893
x33=29.811598790893x_{33} = 29.811598790893
Maxima of the function at points:
x33=45.5311340139913x_{33} = 45.5311340139913
x33=−26.6660542588127x_{33} = -26.6660542588127
x33=−64.3871195905574x_{33} = -64.3871195905574
x33=14.0661939128315x_{33} = 14.0661939128315
x33=39.2444323611642x_{33} = 39.2444323611642
x33=76.9560263103312x_{33} = 76.9560263103312
x33=51.8169824872797x_{33} = 51.8169824872797
x33=58.1022547544956x_{33} = 58.1022547544956
x33=83.2401924707234x_{33} = 83.2401924707234
x33=−70.6716857116195x_{33} = -70.6716857116195
x33=−76.9560263103312x_{33} = -76.9560263103312
x33=−32.9563890398225x_{33} = -32.9563890398225
x33=26.6660542588127x_{33} = 26.6660542588127
x33=−95.8081387868617x_{33} = -95.8081387868617
x33=−51.8169824872797x_{33} = -51.8169824872797
x33=−20.3713029592876x_{33} = -20.3713029592876
x33=−89.5242209304172x_{33} = -89.5242209304172
x33=−4355.81798462425x_{33} = -4355.81798462425
x33=32.9563890398225x_{33} = 32.9563890398225
x33=−45.5311340139913x_{33} = -45.5311340139913
x33=−14.0661939128315x_{33} = -14.0661939128315
x33=−83.2401924707234x_{33} = -83.2401924707234
x33=95.8081387868617x_{33} = 95.8081387868617
x33=−39.2444323611642x_{33} = -39.2444323611642
x33=−58.1022547544956x_{33} = -58.1022547544956
x33=108.375719651675x_{33} = 108.375719651675
x33=20.3713029592876x_{33} = 20.3713029592876
x33=89.5242209304172x_{33} = 89.5242209304172
x33=70.6716857116195x_{33} = 70.6716857116195
x33=−7.72525183693771x_{33} = -7.72525183693771
x33=7.72525183693771x_{33} = 7.72525183693771
x33=64.3871195905574x_{33} = 64.3871195905574
Decreasing at intervals
[98.9500628243319,∞)\left[98.9500628243319, \infty\right)
Increasing at intervals
(−∞,−394.267341680887]\left(-\infty, -394.267341680887\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
−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x=0\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x} = 0
Solve this equation
The roots of this equation
x1=−15.5792364103872x_{1} = -15.5792364103872
x2=25.052825280993x_{2} = 25.052825280993
x3=56.5132704621986x_{3} = 56.5132704621986
x4=−342.42775856009x_{4} = -342.42775856009
x5=15.5792364103872x_{5} = 15.5792364103872
x6=81.6569138240367x_{6} = 81.6569138240367
x7=18.7426455847748x_{7} = 18.7426455847748
x8=87.9418500396598x_{8} = 87.9418500396598
x9=−9.20584014293667x_{9} = -9.20584014293667
x10=−69.0860849466452x_{10} = -69.0860849466452
x11=5.94036999057271x_{11} = 5.94036999057271
x12=62.8000005565198x_{12} = 62.8000005565198
x13=37.6459603230864x_{13} = 37.6459603230864
x14=−87.9418500396598x_{14} = -87.9418500396598
x15=97.368830362901x_{15} = 97.368830362901
x16=−25.052825280993x_{16} = -25.052825280993
x17=−65.9431119046552x_{17} = -65.9431119046552
x18=72.2289377620154x_{18} = 72.2289377620154
x19=9.20584014293667x_{19} = 9.20584014293667
x20=−12.404445021902x_{20} = -12.404445021902
x21=−1288.05143523817x_{21} = -1288.05143523817
x22=−28.2033610039524x_{22} = -28.2033610039524
x23=−43.9367614714198x_{23} = -43.9367614714198
x24=94.2265525745684x_{24} = 94.2265525745684
x25=91.0842274914688x_{25} = 91.0842274914688
x26=−59.6567290035279x_{26} = -59.6567290035279
x27=−1790.70669566846x_{27} = -1790.70669566846
x28=28.2033610039524x_{28} = 28.2033610039524
x29=−37.6459603230864x_{29} = -37.6459603230864
x30=−100.511065295271x_{30} = -100.511065295271
x31=47.0813974121542x_{31} = 47.0813974121542
x32=−75.3716854092873x_{32} = -75.3716854092873
x33=69.0860849466452x_{33} = 69.0860849466452
x34=−5.94036999057271x_{34} = -5.94036999057271
x35=−94.2265525745684x_{35} = -94.2265525745684
x36=59.6567290035279x_{36} = 59.6567290035279
x37=−62.8000005565198x_{37} = -62.8000005565198
x38=53.3695918204908x_{38} = 53.3695918204908
x39=−53.3695918204908x_{39} = -53.3695918204908
x40=75.3716854092873x_{40} = 75.3716854092873
x41=12.404445021902x_{41} = 12.404445021902
x42=2.0815759778181x_{42} = 2.0815759778181
x43=−56.5132704621986x_{43} = -56.5132704621986
x44=84.7994143922025x_{44} = 84.7994143922025
x45=−31.3520917265645x_{45} = -31.3520917265645
x46=−21.8996964794928x_{46} = -21.8996964794928
x47=43.9367614714198x_{47} = 43.9367614714198
x48=−72.2289377620154x_{48} = -72.2289377620154
x49=−84.7994143922025x_{49} = -84.7994143922025
x50=100.511065295271x_{50} = 100.511065295271
x51=−40.7916552312719x_{51} = -40.7916552312719
x52=78.5143405319308x_{52} = 78.5143405319308
x53=−78.5143405319308x_{53} = -78.5143405319308
x54=21.8996964794928x_{54} = 21.8996964794928
x55=40.7916552312719x_{55} = 40.7916552312719
x56=131.931731514843x_{56} = 131.931731514843
x57=−50.2256516491831x_{57} = -50.2256516491831
x58=−47.0813974121542x_{58} = -47.0813974121542
x59=31.3520917265645x_{59} = 31.3520917265645
x60=−91.0842274914688x_{60} = -91.0842274914688
x61=34.499514921367x_{61} = 34.499514921367
x62=−2.0815759778181x_{62} = -2.0815759778181
x63=−18.7426455847748x_{63} = -18.7426455847748
x64=65.9431119046552x_{64} = 65.9431119046552
x65=−34.499514921367x_{65} = -34.499514921367
x66=−97.368830362901x_{66} = -97.368830362901
x67=−81.6569138240367x_{67} = -81.6569138240367
x68=50.2256516491831x_{68} = 50.2256516491831
You also need to calculate the limits of y '' for arguments seeking to indeterminate points of a function:
Points where there is an indetermination:
x1=0x_{1} = 0

lim⁡x→0−(−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x)=−13\lim_{x \to 0^-}\left(\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x}\right) = - \frac{1}{3}
lim⁡x→0+(−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x)=−13\lim_{x \to 0^+}\left(\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x}\right) = - \frac{1}{3}
- limits are equal, then skip the corresponding point

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
[97.368830362901,∞)\left[97.368830362901, \infty\right)
Convex at the intervals
(−∞,−1790.70669566846]\left(-\infty, -1790.70669566846\right]
Vertical asymptotes
Have:
x1=0x_{1} = 0
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(sin⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(sin⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x}\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(x)/x, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(sin⁡(x)x2)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{2}}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(sin⁡(x)x2)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{2}}\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⁡(x)x=sin⁡(x)x\frac{\sin{\left(x \right)}}{x} = \frac{\sin{\left(x \right)}}{x}
- No
sin⁡(x)x=−sin⁡(x)x\frac{\sin{\left(x \right)}}{x} = - \frac{\sin{\left(x \right)}}{x}
- No
so, the function
not is
neither even, nor odd
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