Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ sin(|x+pi/6|)

Gráfico de la función y = sin(|x+pi/6|)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          /|    pi|\
f(x) = sin||x + --||
          \|    6 |/
f(x)=sin⁡(∣x+π6∣)f{\left(x \right)} = \sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} 
f = sin(|x + pi/6|)
Gráfico de la función
02468-8-6-4-2-10102-2
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
sin⁡(∣x+π6∣)=0\sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π6x_{1} = - \frac{\pi}{6}
x2=5π6x_{2} = \frac{5 \pi}{6}
Solución numérica
x1=8.90117918517108x_{1} = 8.90117918517108
x2=90.5825881785057x_{2} = 90.5825881785057
x3=71.733032256967x_{3} = 71.733032256967
x4=−75.9218224617533x_{4} = -75.9218224617533
x5=−60.2138591938044x_{5} = -60.2138591938044
x6=30.8923277602996x_{6} = 30.8923277602996
x7=−6.80678408277789x_{7} = -6.80678408277789
x8=43.4586983746588x_{8} = 43.4586983746588
x9=93.7241808320955x_{9} = 93.7241808320955
x10=−50.789081233035x_{10} = -50.789081233035
x11=−72.7802298081635x_{11} = -72.7802298081635
x12=−19.3731546971371x_{12} = -19.3731546971371
x13=−31.9395253114962x_{13} = -31.9395253114962
x14=37.1755130674792x_{14} = 37.1755130674792
x15=24.60914245312x_{15} = 24.60914245312
x16=−91.6297857297023x_{16} = -91.6297857297023
x17=−9.94837673636768x_{17} = -9.94837673636768
x18=−97.9129710368819x_{18} = -97.9129710368819
x19=−82.2050077689329x_{19} = -82.2050077689329
x20=12.0427718387609x_{20} = 12.0427718387609
x21=78.0162175641465x_{21} = 78.0162175641465
x22=−16.2315620435473x_{22} = -16.2315620435473
x23=74.8746249105567x_{23} = 74.8746249105567
x24=84.2994028713261x_{24} = 84.2994028713261
x25=−22.5147473507269x_{25} = -22.5147473507269
x26=15.1843644923507x_{26} = 15.1843644923507
x27=46.6002910282486x_{27} = 46.6002910282486
x28=−35.081117965086x_{28} = -35.081117965086
x29=40.317105721069x_{29} = 40.317105721069
x30=131.423292675173x_{30} = 131.423292675173
x31=34.0339204138894x_{31} = 34.0339204138894
x32=−3.66519142918809x_{32} = -3.66519142918809
x33=12345.9355298323x_{33} = 12345.9355298323
x34=−69.6386371545737x_{34} = -69.6386371545737
x35=−47.6474885794452x_{35} = -47.6474885794452
x36=59.1666616426078x_{36} = 59.1666616426078
x37=−66.497044500984x_{37} = -66.497044500984
x38=2.61799387799149x_{38} = 2.61799387799149
x39=−38.2227106186758x_{39} = -38.2227106186758
x40=65.4498469497874x_{40} = 65.4498469497874
x41=−41.3643032722656x_{41} = -41.3643032722656
x42=−101.054563690472x_{42} = -101.054563690472
x43=87.4409955249159x_{43} = 87.4409955249159
x44=62.3082542961976x_{44} = 62.3082542961976
x45=100.007366139275x_{45} = 100.007366139275
x46=−13.0899693899575x_{46} = -13.0899693899575
x47=5.75958653158129x_{47} = 5.75958653158129
x48=52.8834763354282x_{48} = 52.8834763354282
x49=49.7418836818384x_{49} = 49.7418836818384
x50=−28.7979326579064x_{50} = -28.7979326579064
x51=68.5914396033772x_{51} = 68.5914396033772
x52=−820.479281362534x_{52} = -820.479281362534
x53=−88.4881930761125x_{53} = -88.4881930761125
x54=−25.6563400043166x_{54} = -25.6563400043166
x55=96.8657734856853x_{55} = 96.8657734856853
x56=−63.3554518473942x_{56} = -63.3554518473942
x57=−94.7713783832921x_{57} = -94.7713783832921
x58=56.025068989018x_{58} = 56.025068989018
x59=−44.5058959258554x_{59} = -44.5058959258554
x60=−79.0634151153431x_{60} = -79.0634151153431
x61=−85.3466004225227x_{61} = -85.3466004225227
x62=21.4675497995303x_{62} = 21.4675497995303
x63=−0.523598775598299x_{63} = -0.523598775598299
x64=27.7507351067098x_{64} = 27.7507351067098
x65=18.3259571459405x_{65} = 18.3259571459405
x66=81.1578102177363x_{66} = 81.1578102177363
x67=−57.0722665402146x_{67} = -57.0722665402146
x68=−53.9306738866248x_{68} = -53.9306738866248
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en sin(|x + pi/6|).
sin⁡(∣π6∣)\sin{\left(\left|{\frac{\pi}{6}}\right| \right)}
Resultado:
f(0)=12f{\left(0 \right)} = \frac{1}{2}
Punto:
(0, 1/2)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
cos⁡(∣x+π6∣)sign⁡(x+π6)=0\cos{\left(\left|{x + \frac{\pi}{6}}\right| \right)} \operatorname{sign}{\left(x + \frac{\pi}{6} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=89.0117918517108x_{1} = 89.0117918517108
x2=−93.2005820564972x_{2} = -93.2005820564972
x3=−55.5014702134197x_{3} = -55.5014702134197
x4=−36.6519142918809x_{4} = -36.6519142918809
x5=−30.3687289847013x_{5} = -30.3687289847013
x6=−68.0678408277789x_{6} = -68.0678408277789
x7=4.18879020478639x_{7} = 4.18879020478639
x8=51.3126800086333x_{8} = 51.3126800086333
x9=32.4631240870945x_{9} = 32.4631240870945
x10=−96.342174710087x_{10} = -96.342174710087
x11=−14.6607657167524x_{11} = -14.6607657167524
x12=85.870199198121x_{12} = 85.870199198121
x13=63.8790506229925x_{13} = 63.8790506229925
x14=−42.9350995990605x_{14} = -42.9350995990605
x15=7.33038285837618x_{15} = 7.33038285837618
x16=82.7286065445312x_{16} = 82.7286065445312
x17=29.3215314335047x_{17} = 29.3215314335047
x18=19.8967534727354x_{18} = 19.8967534727354
x19=95.2949771588904x_{19} = 95.2949771588904
x20=−71.2094334813686x_{20} = -71.2094334813686
x21=98.4365698124802x_{21} = 98.4365698124802
x22=−64.9262481741891x_{22} = -64.9262481741891
x23=−46.0766922526503x_{23} = -46.0766922526503
x24=−24.0855436775217x_{24} = -24.0855436775217
x25=−33.5103216382911x_{25} = -33.5103216382911
x26=−58.6430628670095x_{26} = -58.6430628670095
x27=54.4542726622231x_{27} = 54.4542726622231
x28=73.3038285837618x_{28} = 73.3038285837618
x29=−20.943951023932x_{29} = -20.943951023932
x30=16.7551608191456x_{30} = 16.7551608191456
x31=−90.0589894029074x_{31} = -90.0589894029074
x32=13.6135681655558x_{32} = 13.6135681655558
x33=35.6047167406843x_{33} = 35.6047167406843
x34=−99.4837673636768x_{34} = -99.4837673636768
x35=45.0294947014537x_{35} = 45.0294947014537
x36=92.1533845053006x_{36} = 92.1533845053006
x37=−27.2271363311115x_{37} = -27.2271363311115
x38=67.0206432765823x_{38} = 67.0206432765823
x39=23.0383461263252x_{39} = 23.0383461263252
x40=60.7374579694027x_{40} = 60.7374579694027
x41=10.471975511966x_{41} = 10.471975511966
x42=−5.23598775598299x_{42} = -5.23598775598299
x43=−86.9173967493176x_{43} = -86.9173967493176
x44=−2.0943951023932x_{44} = -2.0943951023932
x45=41.8879020478639x_{45} = 41.8879020478639
x46=−11.5191730631626x_{46} = -11.5191730631626
x47=−74.3510261349584x_{47} = -74.3510261349584
x48=26.1799387799149x_{48} = 26.1799387799149
x49=−83.7758040957278x_{49} = -83.7758040957278
x50=1.0471975511966x_{50} = 1.0471975511966
x51=−17.8023583703422x_{51} = -17.8023583703422
x52=79.5870138909414x_{52} = 79.5870138909414
x53=70.162235930172x_{53} = 70.162235930172
x54=−8.37758040957278x_{54} = -8.37758040957278
x55=−61.7846555205993x_{55} = -61.7846555205993
x56=38.7463093942741x_{56} = 38.7463093942741
x57=76.4454212373516x_{57} = 76.4454212373516
x58=−52.3598775598299x_{58} = -52.3598775598299
x59=−39.7935069454707x_{59} = -39.7935069454707
x60=−77.4926187885482x_{60} = -77.4926187885482
x61=−80.634211442138x_{61} = -80.634211442138
x62=104.71975511966x_{62} = 104.71975511966
x63=48.1710873550435x_{63} = 48.1710873550435
x64=57.5958653158129x_{64} = 57.5958653158129
x65=−49.2182849062401x_{65} = -49.2182849062401
Signos de extremos en los puntos:
                       /                   pi\ 
(89.01179185171081, sin|89.0117918517108 + --|)
                       \                   6 / 

                       /                   pi\ 
(-93.2005820564972, sin|93.2005820564972 - --|)
                       \                   6 / 

                        /                   pi\ 
(-55.50147021341968, sin|55.5014702134197 - --|)
                        \                   6 / 

                        /                   pi\ 
(-36.65191429188092, sin|36.6519142918809 - --|)
                        \                   6 / 

                         /                   pi\ 
(-30.368728984701335, sin|30.3687289847013 - --|)
                         \                   6 / 

                        /                   pi\ 
(-68.06784082777885, sin|68.0678408277789 - --|)
                        \                   6 / 

                       /                   pi\ 
(4.188790204786391, sin|4.18879020478639 + --|)
                       \                   6 / 

                        /                   pi\ 
(51.312680008633286, sin|51.3126800086333 + --|)
                        \                   6 / 

                       /                   pi\ 
(32.46312408709453, sin|32.4631240870945 + --|)
                       \                   6 / 

                      /                  pi\ 
(-96.342174710087, sin|96.342174710087 - --|)
                      \                  6 / 

                         /                   pi\ 
(-14.660765716752369, sin|14.6607657167524 - --|)
                         \                   6 / 

                       /                  pi\ 
(85.87019919812101, sin|85.870199198121 + --|)
                       \                  6 / 

                        /                   pi\ 
(63.879050622992466, sin|63.8790506229925 + --|)
                        \                   6 / 

                        /                   pi\ 
(-42.93509959906051, sin|42.9350995990605 - --|)
                        \                   6 / 

                        /                   pi\ 
(7.3303828583761845, sin|7.33038285837618 + --|)
                        \                   6 / 

                       /                   pi\ 
(82.72860654453122, sin|82.7286065445312 + --|)
                       \                   6 / 

                        /                   pi\ 
(29.321531433504738, sin|29.3215314335047 + --|)
                        \                   6 / 

                       /                   pi\ 
(19.89675347273536, sin|19.8967534727354 + --|)
                       \                   6 / 

                       /                   pi\ 
(95.29497715889039, sin|95.2949771588904 + --|)
                       \                   6 / 

                        /                   pi\ 
(-71.20943348136865, sin|71.2094334813686 - --|)
                        \                   6 / 

                       /                   pi\ 
(98.43656981248019, sin|98.4365698124802 + --|)
                       \                   6 / 

                        /                   pi\ 
(-64.92624817418906, sin|64.9262481741891 - --|)
                        \                   6 / 

                         /                   pi\ 
(-46.076692252650304, sin|46.0766922526503 - --|)
                         \                   6 / 

                        /                   pi\ 
(-24.08554367752175, sin|24.0855436775217 - --|)
                        \                   6 / 

                        /                   pi\ 
(-33.51032163829113, sin|33.5103216382911 - --|)
                        \                   6 / 

                         /                   pi\ 
(-58.643062867009476, sin|58.6430628670095 - --|)
                         \                   6 / 

                       /                   pi\ 
(54.45427266222308, sin|54.4542726622231 + --|)
                       \                   6 / 

                       /                   pi\ 
(73.30382858376184, sin|73.3038285837618 + --|)
                       \                   6 / 

                         /                  pi\ 
(-20.943951023931955, sin|20.943951023932 - --|)
                         \                  6 / 

                        /                   pi\ 
(16.755160819145566, sin|16.7551608191456 + --|)
                        \                   6 / 

                       /                   pi\ 
(-90.0589894029074, sin|90.0589894029074 - --|)
                       \                   6 / 

                       /                   pi\ 
(13.61356816555577, sin|13.6135681655558 + --|)
                       \                   6 / 

                        /                   pi\ 
(35.604716740684324, sin|35.6047167406843 + --|)
                        \                   6 / 

                        /                   pi\ 
(-99.48376736367679, sin|99.4837673636768 - --|)
                        \                   6 / 

                      /                   pi\ 
(45.0294947014537, sin|45.0294947014537 + --|)
                      \                   6 / 

                       /                   pi\ 
(92.15338450530061, sin|92.1533845053006 + --|)
                       \                   6 / 

                        /                   pi\ 
(-27.22713633111154, sin|27.2271363311115 - --|)
                        \                   6 / 

                       /                   pi\ 
(67.02064327658226, sin|67.0206432765823 + --|)
                       \                   6 / 

                        /                   pi\ 
(23.038346126325152, sin|23.0383461263252 + --|)
                        \                   6 / 

                       /                   pi\ 
(60.73745796940267, sin|60.7374579694027 + --|)
                       \                   6 / 

                        /                  pi\ 
(10.471975511965978, sin|10.471975511966 + --|)
                        \                  6 / 

                        /                   pi\ 
(-5.235987755982989, sin|5.23598775598299 - --|)
                        \                   6 / 

                        /                   pi\ 
(-86.91739674931762, sin|86.9173967493176 - --|)
                        \                   6 / 

                         /                  pi\ 
(-2.0943951023931957, sin|2.0943951023932 - --|)
                         \                  6 / 

                       /                   pi\ 
(41.88790204786391, sin|41.8879020478639 + --|)
                       \                   6 / 

                         /                   pi\ 
(-11.519173063162576, sin|11.5191730631626 - --|)
                         \                   6 / 

                        /                   pi\ 
(-74.35102613495845, sin|74.3510261349584 - --|)
                        \                   6 / 

                        /                   pi\ 
(26.179938779914945, sin|26.1799387799149 + --|)
                        \                   6 / 

                        /                   pi\ 
(-83.77580409572782, sin|83.7758040957278 - --|)
                        \                   6 / 

                        /                  pi\ 
(1.0471975511965979, sin|1.0471975511966 + --|)
                        \                  6 / 

                         /                   pi\ 
(-17.802358370342162, sin|17.8023583703422 - --|)
                         \                   6 / 

                       /                   pi\ 
(79.58701389094144, sin|79.5870138909414 + --|)
                       \                   6 / 

                       /                  pi\ 
(70.16223593017205, sin|70.162235930172 + --|)
                       \                  6 / 

                        /                   pi\ 
(-8.377580409572783, sin|8.37758040957278 - --|)
                        \                   6 / 

                         /                   pi\ 
(-61.784655520599266, sin|61.7846555205993 - --|)
                         \                   6 / 

                        /                   pi\ 
(38.746309394274114, sin|38.7463093942741 + --|)
                        \                   6 / 

                       /                   pi\ 
(76.44542123735164, sin|76.4454212373516 + --|)
                       \                   6 / 

                        /                   pi\ 
(-52.35987755982989, sin|52.3598775598299 - --|)
                        \                   6 / 

                        /                   pi\ 
(-39.79350694547072, sin|39.7935069454707 - --|)
                        \                   6 / 

                        /                   pi\ 
(-77.49261878854823, sin|77.4926187885482 - --|)
                        \                   6 / 

                        /                  pi\ 
(-80.63421144213802, sin|80.634211442138 - --|)
                        \                  6 / 

                        /                  pi\ 
(104.71975511965978, sin|104.71975511966 + --|)
                        \                  6 / 

                      /                   pi\ 
(48.1710873550435, sin|48.1710873550435 + --|)
                      \                   6 / 

                       /                   pi\ 
(57.59586531581287, sin|57.5958653158129 + --|)
                       \                   6 / 

                        /                   pi\ 
(-49.21828490624009, sin|49.2182849062401 - --|)
                        \                   6 /


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=−93.2005820564972x_{1} = -93.2005820564972
x2=−55.5014702134197x_{2} = -55.5014702134197
x3=−36.6519142918809x_{3} = -36.6519142918809
x4=−30.3687289847013x_{4} = -30.3687289847013
x5=−68.0678408277789x_{5} = -68.0678408277789
x6=4.18879020478639x_{6} = 4.18879020478639
x7=85.870199198121x_{7} = 85.870199198121
x8=−42.9350995990605x_{8} = -42.9350995990605
x9=29.3215314335047x_{9} = 29.3215314335047
x10=98.4365698124802x_{10} = 98.4365698124802
x11=−24.0855436775217x_{11} = -24.0855436775217
x12=54.4542726622231x_{12} = 54.4542726622231
x13=73.3038285837618x_{13} = 73.3038285837618
x14=16.7551608191456x_{14} = 16.7551608191456
x15=35.6047167406843x_{15} = 35.6047167406843
x16=−99.4837673636768x_{16} = -99.4837673636768
x17=92.1533845053006x_{17} = 92.1533845053006
x18=67.0206432765823x_{18} = 67.0206432765823
x19=23.0383461263252x_{19} = 23.0383461263252
x20=60.7374579694027x_{20} = 60.7374579694027
x21=10.471975511966x_{21} = 10.471975511966
x22=−5.23598775598299x_{22} = -5.23598775598299
x23=−86.9173967493176x_{23} = -86.9173967493176
x24=41.8879020478639x_{24} = 41.8879020478639
x25=−11.5191730631626x_{25} = -11.5191730631626
x26=−74.3510261349584x_{26} = -74.3510261349584
x27=−17.8023583703422x_{27} = -17.8023583703422
x28=79.5870138909414x_{28} = 79.5870138909414
x29=−61.7846555205993x_{29} = -61.7846555205993
x30=−80.634211442138x_{30} = -80.634211442138
x31=104.71975511966x_{31} = 104.71975511966
x32=48.1710873550435x_{32} = 48.1710873550435
x33=−49.2182849062401x_{33} = -49.2182849062401
Puntos máximos de la función:
x33=89.0117918517108x_{33} = 89.0117918517108
x33=51.3126800086333x_{33} = 51.3126800086333
x33=32.4631240870945x_{33} = 32.4631240870945
x33=−96.342174710087x_{33} = -96.342174710087
x33=−14.6607657167524x_{33} = -14.6607657167524
x33=63.8790506229925x_{33} = 63.8790506229925
x33=7.33038285837618x_{33} = 7.33038285837618
x33=82.7286065445312x_{33} = 82.7286065445312
x33=19.8967534727354x_{33} = 19.8967534727354
x33=95.2949771588904x_{33} = 95.2949771588904
x33=−71.2094334813686x_{33} = -71.2094334813686
x33=−64.9262481741891x_{33} = -64.9262481741891
x33=−46.0766922526503x_{33} = -46.0766922526503
x33=−33.5103216382911x_{33} = -33.5103216382911
x33=−58.6430628670095x_{33} = -58.6430628670095
x33=−20.943951023932x_{33} = -20.943951023932
x33=−90.0589894029074x_{33} = -90.0589894029074
x33=13.6135681655558x_{33} = 13.6135681655558
x33=45.0294947014537x_{33} = 45.0294947014537
x33=−27.2271363311115x_{33} = -27.2271363311115
x33=−2.0943951023932x_{33} = -2.0943951023932
x33=26.1799387799149x_{33} = 26.1799387799149
x33=−83.7758040957278x_{33} = -83.7758040957278
x33=1.0471975511966x_{33} = 1.0471975511966
x33=70.162235930172x_{33} = 70.162235930172
x33=−8.37758040957278x_{33} = -8.37758040957278
x33=38.7463093942741x_{33} = 38.7463093942741
x33=76.4454212373516x_{33} = 76.4454212373516
x33=−52.3598775598299x_{33} = -52.3598775598299
x33=−39.7935069454707x_{33} = -39.7935069454707
x33=−77.4926187885482x_{33} = -77.4926187885482
x33=57.5958653158129x_{33} = 57.5958653158129
Decrece en los intervalos
[104.71975511966,∞)\left[104.71975511966, \infty\right)
Crece en los intervalos
(−∞,−99.4837673636768]\left(-\infty, -99.4837673636768\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
−sin⁡(∣x+π6∣)sign⁡2(x+π6)+2cos⁡(∣x+π6∣)δ(x+π6)=0- \sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} \operatorname{sign}^{2}{\left(x + \frac{\pi}{6} \right)} + 2 \cos{\left(\left|{x + \frac{\pi}{6}}\right| \right)} \delta\left(x + \frac{\pi}{6}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=5π6x_{1} = \frac{5 \pi}{6}

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[5π6,∞)\left[\frac{5 \pi}{6}, \infty\right)
Convexa en los intervalos
(−∞,5π6]\left(-\infty, \frac{5 \pi}{6}\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞sin⁡(∣x+π6∣)=⟨−1,1⟩\lim_{x \to -\infty} \sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞sin⁡(∣x+π6∣)=⟨−1,1⟩\lim_{x \to \infty} \sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(|x + pi/6|), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(∣x+π6∣)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(∣x+π6∣)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
sin⁡(∣x+π6∣)=sin⁡(x2−πx3+π236)\sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} = \sin{\left(\sqrt{x^{2} - \frac{\pi x}{3} + \frac{\pi^{2}}{36}} \right)}
- No
sin⁡(∣x+π6∣)=−sin⁡(x2−πx3+π236)\sin{\left(\left|{x + \frac{\pi}{6}}\right| \right)} = - \sin{\left(\sqrt{x^{2} - \frac{\pi x}{3} + \frac{\pi^{2}}{36}} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор