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Trazado el gráfico de la función/ tan(x^2)+sin(3*x)^(2)

Gráfico de la función y = tan(x^2)+sin(3*x)^(2)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          / 2\      2     
f(x) = tan\x / + sin (3*x)
f(x)=sin⁡2(3x)+tan⁡(x2)f{\left(x \right)} = \sin^{2}{\left(3 x \right)} + \tan{\left(x^{2} \right)} 
f = sin(3*x)^2 + tan(x^2)
Gráfico de la función
02468-8-6-4-2-1010-200200
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⁡2(3x)+tan⁡(x2)=0\sin^{2}{\left(3 x \right)} + \tan{\left(x^{2} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−26.9897365577574x_{1} = -26.9897365577574
x2=22.0657570528061x_{2} = 22.0657570528061
x3=66.2211006687906x_{3} = 66.2211006687906
x4=−7.30769805667146x_{4} = -7.30769805667146
x5=52.2488031743576x_{5} = 52.2488031743576
x6=−81.3751425327185x_{6} = -81.3751425327185
x7=90.1683883523412x_{7} = 90.1683883523412
x8=−21.9955698433714x_{8} = -21.9955698433714
x9=−95.3342212991286x_{9} = -95.3342212991286
x10=−83.9610766279376x_{10} = -83.9610766279376
x11=−19.56156501682x_{11} = -19.56156501682
x12=39.8697197987395x_{12} = 39.8697197987395
x13=74.2523413402936x_{13} = 74.2523413402936
x14=76.5033153468676x_{14} = 76.5033153468676
x15=6.58931607437317x_{15} = 6.58931607437317
x16=4.3238248391816x_{16} = 4.3238248391816
x17=−47.7499613752264x_{17} = -47.7499613752264
x18=−3.89498568987615x_{18} = -3.89498568987615
x19=−74.2094585643875x_{19} = -74.2094585643875
x20=−85.9227449316417x_{20} = -85.9227449316417
x21=92.2354249359452x_{21} = 92.2354249359452
x22=24.2957762692694x_{22} = 24.2957762692694
x23=46.2512650732181x_{23} = 46.2512650732181
x24=−77.8028116427924x_{24} = -77.8028116427924
x25=−71.7734904928149x_{25} = -71.7734904928149
x26=20.0482769377562x_{26} = 20.0482769377562
x27=32.1906291750018x_{27} = 32.1906291750018
x28=57.6251312046399x_{28} = 57.6251312046399
x29=−33.8986984283265x_{29} = -33.8986984283265
x30=14.1519438450597x_{30} = 14.1519438450597
x31=16.2206326131383x_{31} = 16.2206326131383
x32=62.0572588135703x_{32} = 62.0572588135703
x33=72.0829476768963x_{33} = 72.0829476768963
x34=78.4897496909535x_{34} = 78.4897496909535
x35=70.2742860035055x_{35} = 70.2742860035055
x36=−15.7533301995739x_{36} = -15.7533301995739
x37=57.3762183284439x_{37} = 57.3762183284439
x38=−1.53669650151876x_{38} = -1.53669650151876
x39=96.2686370477793x_{39} = 96.2686370477793
x40=81.6096243869309x_{40} = 81.6096243869309
x41=48.2479836251242x_{41} = 48.2479836251242
x42=50.2577352594784x_{42} = 50.2577352594784
x43=0x_{43} = 0
x44=8.09014212247502x_{44} = 8.09014212247502
x45=−51.1540796997353x_{45} = -51.1540796997353
x46=42.2348745537244x_{46} = 42.2348745537244
x47=59.9974973352967x_{47} = 59.9974973352967
x48=−65.7209930054483x_{48} = -65.7209930054483
x49=−13.7254334046838x_{49} = -13.7254334046838
x50=48.6297538496154x_{50} = 48.6297538496154
x51=−98.2054048253549x_{51} = -98.2054048253549
x52=37.8870639549038x_{52} = 37.8870639549038
x53=−57.5431477899333x_{53} = -57.5431477899333
x54=67.7206385753793x_{54} = 67.7206385753793
x55=33.5363102279478x_{55} = 33.5363102279478
x56=−61.6277755711363x_{56} = -61.6277755711363
x57=28.2481571034765x_{57} = 28.2481571034765
x58=9.98761793500696x_{58} = 9.98761793500696
x59=−53.4094193939551x_{59} = -53.4094193939551
x60=54.1934293121096x_{60} = 54.1934293121096
x61=−91.9266421020421x_{61} = -91.9266421020421
x62=−69.6633188663068x_{62} = -69.6633188663068
x63=91.2757947784565x_{63} = 91.2757947784565
x64=−64.1002386598619x_{64} = -64.1002386598619
x65=−45.769832676704x_{65} = -45.769832676704
x66=−75.4902307411747x_{66} = -75.4902307411747
x67=−44.7285382494702x_{67} = -44.7285382494702
x68=20.3452795484772x_{68} = 20.3452795484772
x69=−95.5297319807192x_{69} = -95.5297319807192
x70=−57.7860634268949x_{70} = -57.7860634268949
x71=38.2518050870199x_{71} = 38.2518050870199
x72=84.0901019641939x_{72} = 84.0901019641939
x73=78.4695986137623x_{73} = 78.4695986137623
x74=−35.7552786166496x_{74} = -35.7552786166496
x75=17.8129126147077x_{75} = 17.8129126147077
x76=−13.8305883096509x_{76} = -13.8305883096509
x77=12.1200903318687x_{77} = 12.1200903318687
x78=−41.754438675669x_{78} = -41.754438675669
x79=97.388234451273x_{79} = 97.388234451273
x80=99.5574047745468x_{80} = 99.5574047745468
x81=95.8396239341347x_{81} = 95.8396239341347
x82=−5.81246554120487x_{82} = -5.81246554120487
x83=30.2867267291309x_{83} = 30.2867267291309
x84=80.425167890787x_{84} = 80.425167890787
x85=−31.6030125957562x_{85} = -31.6030125957562
x86=−39.7517990995002x_{86} = -39.7517990995002
x87=−29.752028712372x_{87} = -29.752028712372
x88=−26.1090224241995x_{88} = -26.1090224241995
x89=−52.1256364263351x_{89} = -52.1256364263351
x90=−23.836874703449x_{90} = -23.836874703449
x91=−8.09014212247502x_{91} = -8.09014212247502
x92=−87.6571140019108x_{92} = -87.6571140019108
x93=−11.7415677003213x_{93} = -11.7415677003213
x94=−67.6737306024849x_{94} = -67.6737306024849
x95=53.5832682799867x_{95} = 53.5832682799867
x96=3.06053322946611x_{96} = 3.06053322946611
x97=−59.3386694875448x_{97} = -59.3386694875448
x98=−79.8752147967889x_{98} = -79.8752147967889
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(3*x)^2.
tan⁡(02)+sin⁡2(0⋅3)\tan{\left(0^{2} \right)} + \sin^{2}{\left(0 \cdot 3 \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⁡2(3x)+tan⁡(x2))y = \lim_{x \to -\infty}\left(\sin^{2}{\left(3 x \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⁡2(3x)+tan⁡(x2))y = \lim_{x \to \infty}\left(\sin^{2}{\left(3 x \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(3*x)^2, 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⁡2(3x)+tan⁡(x2)x)y = x \lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(3 x \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⁡2(3x)+tan⁡(x2)x)y = x \lim_{x \to \infty}\left(\frac{\sin^{2}{\left(3 x \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⁡2(3x)+tan⁡(x2)=sin⁡2(3x)+tan⁡(x2)\sin^{2}{\left(3 x \right)} + \tan{\left(x^{2} \right)} = \sin^{2}{\left(3 x \right)} + \tan{\left(x^{2} \right)}
- Sí
sin⁡2(3x)+tan⁡(x2)=−sin⁡2(3x)−tan⁡(x2)\sin^{2}{\left(3 x \right)} + \tan{\left(x^{2} \right)} = - \sin^{2}{\left(3 x \right)} - \tan{\left(x^{2} \right)}
- No
es decir, función
es
par
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