Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ tan(x^2)+sin(tan(x))

Gráfico de la función y = tan(x^2)+sin(tan(x))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          / 2\              
f(x) = tan\x / + sin(tan(x))
f(x)=sin⁡(tan⁡(x))+tan⁡(x2)f{\left(x \right)} = \sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)} 
f = sin(tan(x)) + tan(x^2)
Gráfico de la función
1.00001.01001.00101.00201.00301.00401.00501.00601.00701.00801.00902.552.57
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⁡(tan⁡(x))+tan⁡(x2)=0\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−29.7517855005631x_{1} = -29.7517855005631
x2=−79.3900002672671x_{2} = -79.3900002672671
x3=9.99940933242916x_{3} = 9.99940933242916
x4=−70.3229652231929x_{4} = -70.3229652231929
x5=8.07498146107138x_{5} = 8.07498146107138
x6=−22.8527359831016x_{6} = -22.8527359831016
x7=−75.9713580193894x_{7} = -75.9713580193894
x8=121.735749388089x_{8} = 121.735749388089
x9=32.6277457795758x_{9} = 32.6277457795758
x10=48.342056298757x_{10} = 48.342056298757
x11=−38.9546461464997x_{11} = -38.9546461464997
x12=−65.7705984879516x_{12} = -65.7705984879516
x13=−77.8427474542381x_{13} = -77.8427474542381
x14=57.9304504513085x_{14} = 57.9304504513085
x15=63.433549411364x_{15} = 63.433549411364
x16=−23.9049523585194x_{16} = -23.9049523585194
x17=−4.05902275504687x_{17} = -4.05902275504687
x18=−11.7259556828163x_{18} = -11.7259556828163
x19=70.2932344207069x_{19} = 70.2932344207069
x20=−59.9519869692351x_{20} = -59.9519869692351
x21=−86.0350006463707x_{21} = -86.0350006463707
x22=−92.0353496457271x_{22} = -92.0353496457271
x23=−21.9956767760921x_{23} = -21.9956767760921
x24=−27.7915044603573x_{24} = -27.7915044603573
x25=−13.7499812780325x_{25} = -13.7499812780325
x26=−9.89136200718152x_{26} = -9.89136200718152
x27=−47.863243426828x_{27} = -47.863243426828
x28=80.1510215917361x_{28} = 80.1510215917361
x29=−7.53038148207774x_{29} = -7.53038148207774
x30=62.1170470894082x_{30} = 62.1170470894082
x31=−35.7227467887821x_{31} = -35.7227467887821
x32=14.0937948235595x_{32} = 14.0937948235595
x33=92.266320553933x_{33} = 92.266320553933
x34=21.9255385110948x_{34} = 21.9255385110948
x35=60.4917015163094x_{35} = 60.4917015163094
x36=0x_{36} = 0
x37=−54.0581665056789x_{37} = -54.0581665056789
x38=20.0395426785993x_{38} = 20.0395426785993
x39=78.2511898440365x_{39} = 78.2511898440365
x40=−64.1708750077503x_{40} = -64.1708750077503
x41=−5.84215363619943x_{41} = -5.84215363619943
x42=−100.311031825817x_{42} = -100.311031825817
x43=−89.8212780504925x_{43} = -89.8212780504925
x44=53.2635075918146x_{44} = 53.2635075918146
x45=46.2956956022564x_{45} = 46.2956956022564
x46=68.7636612768393x_{46} = 68.7636612768393
x47=−58.8059473775428x_{47} = -58.8059473775428
x48=81.1497672462304x_{48} = 81.1497672462304
x49=30.2459453457176x_{49} = 30.2459453457176
x50=4.25695432057086x_{50} = 4.25695432057086
x51=12.0421515175209x_{51} = 12.0421515175209
x52=−61.7505619169245x_{52} = -61.7505619169245
x53=−18.4082870592256x_{53} = -18.4082870592256
x54=86.2180573951011x_{54} = 86.2180573951011
x55=−55.6776808079715x_{55} = -55.6776808079715
x56=93.6583242344403x_{56} = 93.6583242344403
x57=74.102141763322x_{57} = 74.102141763322
x58=54.2488665991577x_{58} = 54.2488665991577
x59=95.6180381144342x_{59} = 95.6180381144342
x60=−51.4669756672221x_{60} = -51.4669756672221
x61=−73.4689283978412x_{61} = -73.4689283978412
x62=59.9996724290719x_{62} = 59.9996724290719
x63=−83.9957880803522x_{63} = -83.9957880803522
x64=3.49566502739981x_{64} = 3.49566502739981
x65=−49.7502017398012x_{65} = -49.7502017398012
x66=−45.7500081449512x_{66} = -45.7500081449512
x67=−81.8801327595732x_{67} = -81.8801327595732
x68=−15.7554199730604x_{68} = -15.7554199730604
x69=−93.7702428422148x_{69} = -93.7702428422148
x70=29.1118458248098x_{70} = 29.1118458248098
x71=19.2438008922598x_{71} = 19.2438008922598
x72=−67.8207129994151x_{72} = -67.8207129994151
x73=−97.9860606085831x_{73} = -97.9860606085831
x74=84.0788664515024x_{74} = 84.0788664515024
x75=−39.6653698855939x_{75} = -39.6653698855939
x76=65.7262095506622x_{76} = 65.7262095506622
x77=64.8394196857057x_{77} = 64.8394196857057
x78=87.1073316070173x_{78} = 87.1073316070173
x79=40.0754334162764x_{79} = 40.0754334162764
x80=28.2487193644038x_{80} = 28.2487193644038
x81=16.2294781389572x_{81} = 16.2294781389572
x82=38.4173700279838x_{82} = 38.4173700279838
x83=−73.7219863555296x_{83} = -73.7219863555296
x84=24.2534447752652x_{84} = 24.2534447752652
x85=−26.4065921222657x_{85} = -26.4065921222657
x86=42.2458639356195x_{86} = 42.2458639356195
x87=6.82693512063946x_{87} = 6.82693512063946
x88=76.1286779318696x_{88} = 76.1286779318696
x89=34.0547972484487x_{89} = 34.0547972484487
x90=−41.7654669548989x_{90} = -41.7654669548989
x91=94.3400226591415x_{91} = 94.3400226591415
x92=36.247973020363x_{92} = 36.247973020363
x93=−95.7249728670535x_{93} = -95.7249728670535
x94=43.3145220176448x_{94} = 43.3145220176448
x95=89.2418140427901x_{95} = 89.2418140427901
x96=72.4312501521193x_{96} = 72.4312501521193
x97=22.0651961553871x_{97} = 22.0651961553871
x98=−1.85311933712728x_{98} = -1.85311933712728
x99=−33.9937102808544x_{99} = -33.9937102808544
x100=−28.696815456598x_{100} = -28.696815456598
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 tan(x^2) + sin(tan(x)).
tan⁡(02)+sin⁡(tan⁡(0))\tan{\left(0^{2} \right)} + \sin{\left(\tan{\left(0 \right)} \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(sin⁡(tan⁡(x))+tan⁡(x2))y = \lim_{x \to -\infty}\left(\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(sin⁡(tan⁡(x))+tan⁡(x2))y = \lim_{x \to \infty}\left(\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x^2) + sin(tan(x)), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(sin⁡(tan⁡(x))+tan⁡(x2)x)y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(sin⁡(tan⁡(x))+tan⁡(x2)x)y = x \lim_{x \to \infty}\left(\frac{\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)}}{x}\right)
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⁡(tan⁡(x))+tan⁡(x2)=−sin⁡(tan⁡(x))+tan⁡(x2)\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)} = - \sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)}
- No
sin⁡(tan⁡(x))+tan⁡(x2)=sin⁡(tan⁡(x))−tan⁡(x2)\sin{\left(\tan{\left(x \right)} \right)} + \tan{\left(x^{2} \right)} = \sin{\left(\tan{\left(x \right)} \right)} - \tan{\left(x^{2} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор