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Trazado el gráfico de la función/ tan(2𝑥+2)/(√𝑥√(3−𝑥))

Gráfico de la función y = tan(2𝑥+2)/(√𝑥√(3−𝑥))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
         tan(2*x + 2) 
f(x) = ---------------
         ___   _______
       \/ x *\/ 3 - x
f(x)=tan⁡(2x+2)x3−xf{\left(x \right)} = \frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}} 
f = tan(2*x + 2)/((sqrt(x)*sqrt(3 - x)))
Gráfico de la función
02468-8-6-4-2-1010-1000500
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
x2=3x_{2} = 3
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:
tan⁡(2x+2)x3−x=0\frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−1x_{1} = -1
Solución numérica
x1=52.4070751110265x_{1} = 52.4070751110265
x2=−49.6946861306418x_{2} = -49.6946861306418
x3=−68.5442420521806x_{3} = -68.5442420521806
x4=−43.4115008234622x_{4} = -43.4115008234622
x5=50.8362787842316x_{5} = 50.8362787842316
x6=14.707963267949x_{6} = 14.707963267949
x7=68.1150383789755x_{7} = 68.1150383789755
x8=11.5663706143592x_{8} = 11.5663706143592
x9=−11.9955742875643x_{9} = -11.9955742875643
x10=−73.2566310325652x_{10} = -73.2566310325652
x11=66.5442420521806x_{11} = 66.5442420521806
x12=−55.9778714378214x_{12} = -55.9778714378214
x13=−57.5486677646163x_{13} = -57.5486677646163
x14=−33.9867228626928x_{14} = -33.9867228626928
x15=24.1327412287183x_{15} = 24.1327412287183
x16=6.85398163397448x_{16} = 6.85398163397448
x17=31.9867228626928x_{17} = 31.9867228626928
x18=−54.4070751110265x_{18} = -54.4070751110265
x19=−81.1106126665397x_{19} = -81.1106126665397
x20=47.6946861306418x_{20} = 47.6946861306418
x21=−18.2787595947439x_{21} = -18.2787595947439
x22=75.9690200129499x_{22} = 75.9690200129499
x23=−48.1238898038469x_{23} = -48.1238898038469
x24=−21.4203522483337x_{24} = -21.4203522483337
x25=−93.6769832808989x_{25} = -93.6769832808989
x26=−24.5619449019235x_{26} = -24.5619449019235
x27=−62.261056745001x_{27} = -62.261056745001
x28=−35.5575191894877x_{28} = -35.5575191894877
x29=22.5619449019235x_{29} = 22.5619449019235
x30=3.71238898038469x_{30} = 3.71238898038469
x31=−51.2654824574367x_{31} = -51.2654824574367
x32=−37.1283155162826x_{32} = -37.1283155162826
x33=41.4115008234622x_{33} = 41.4115008234622
x34=28.845130209103x_{34} = 28.845130209103
x35=58.6902604182061x_{35} = 58.6902604182061
x36=−77.9690200129499x_{36} = -77.9690200129499
x37=−46.553093477052x_{37} = -46.553093477052
x38=74.398223686155x_{38} = 74.398223686155
x39=−5.71238898038469x_{39} = -5.71238898038469
x40=−84.2522053201295x_{40} = -84.2522053201295
x41=83.8230016469244x_{41} = 83.8230016469244
x42=−87.3937979737193x_{42} = -87.3937979737193
x43=61.8318530717959x_{43} = 61.8318530717959
x44=39.8407044966673x_{44} = 39.8407044966673
x45=19.4203522483337x_{45} = 19.4203522483337
x46=−32.4159265358979x_{46} = -32.4159265358979
x47=90.106186954104x_{47} = 90.106186954104
x48=36.6991118430775x_{48} = 36.6991118430775
x49=38.2699081698724x_{49} = 38.2699081698724
x50=94.8185759344887x_{50} = 94.8185759344887
x51=17.8495559215388x_{51} = 17.8495559215388
x52=46.1238898038469x_{52} = 46.1238898038469
x53=53.9778714378214x_{53} = 53.9778714378214
x54=−2.5707963267949x_{54} = -2.5707963267949
x55=2.14159265358979x_{55} = 2.14159265358979
x56=80.6814089933346x_{56} = 80.6814089933346
x57=77.5398163397448x_{57} = 77.5398163397448
x58=−29.2743338823081x_{58} = -29.2743338823081
x59=63.4026493985908x_{59} = 63.4026493985908
x60=−19.8495559215388x_{60} = -19.8495559215388
x61=−40.2699081698724x_{61} = -40.2699081698724
x62=69.6858347057703x_{62} = 69.6858347057703
x63=−76.398223686155x_{63} = -76.398223686155
x64=−90.5353906273091x_{64} = -90.5353906273091
x65=8.42477796076938x_{65} = 8.42477796076938
x66=−4.14159265358979x_{66} = -4.14159265358979
x67=−27.7035375555132x_{67} = -27.7035375555132
x68=−10.4247779607694x_{68} = -10.4247779607694
x69=−71.6858347057703x_{69} = -71.6858347057703
x70=9.99557428756428x_{70} = 9.99557428756428
x71=−98.3893722612836x_{71} = -98.3893722612836
x72=82.2522053201295x_{72} = 82.2522053201295
x73=−13.5663706143592x_{73} = -13.5663706143592
x74=72.8274273593601x_{74} = 72.8274273593601
x75=33.5575191894877x_{75} = 33.5575191894877
x76=−63.8318530717959x_{76} = -63.8318530717959
x77=−26.1327412287183x_{77} = -26.1327412287183
x78=−59.1194640914112x_{78} = -59.1194640914112
x79=99.5309649148734x_{79} = 99.5309649148734
x80=−41.8407044966673x_{80} = -41.8407044966673
x81=25.7035375555132x_{81} = 25.7035375555132
x82=44.553093477052x_{82} = 44.553093477052
x83=−99.9601685880785x_{83} = -99.9601685880785
x84=−79.5398163397448x_{84} = -79.5398163397448
x85=−15.1371669411541x_{85} = -15.1371669411541
x86=30.4159265358979x_{86} = 30.4159265358979
x87=91.6769832808989x_{87} = 91.6769832808989
x88=97.9601685880785x_{88} = 97.9601685880785
x89=−95.2477796076938x_{89} = -95.2477796076938
x90=16.2787595947439x_{90} = 16.2787595947439
x91=−85.8230016469244x_{91} = -85.8230016469244
x92=85.3937979737193x_{92} = 85.3937979737193
x93=55.5486677646163x_{93} = 55.5486677646163
x94=−92.106186954104x_{94} = -92.106186954104
x95=−70.1150383789755x_{95} = -70.1150383789755
x96=96.3893722612836x_{96} = 96.3893722612836
x97=−65.4026493985908x_{97} = -65.4026493985908
x98=88.5353906273091x_{98} = 88.5353906273091
x99=−7.28318530717959x_{99} = -7.28318530717959
x100=60.261056745001x_{100} = 60.261056745001
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(2*x + 2)/((sqrt(x)*sqrt(3 - x))).
tan⁡(0⋅2+2)03−0\frac{\tan{\left(0 \cdot 2 + 2 \right)}}{\sqrt{0} \sqrt{3 - 0}}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
Asíntotas verticales
Hay:
x1=0x_{1} = 0
x2=3x_{2} = 3
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→−∞(tan⁡(2x+2)x3−x)y = \lim_{x \to -\infty}\left(\frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(tan⁡(2x+2)x3−x)y = \lim_{x \to \infty}\left(\frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(2*x + 2)/((sqrt(x)*sqrt(3 - 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→−∞(1x3−xtan⁡(2x+2)x)y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{\sqrt{x} \sqrt{3 - x}} \tan{\left(2 x + 2 \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(1x3−xtan⁡(2x+2)x)y = x \lim_{x \to \infty}\left(\frac{\frac{1}{\sqrt{x} \sqrt{3 - x}} \tan{\left(2 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:
tan⁡(2x+2)x3−x=−tan⁡(2x−2)−xx+3\frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}} = - \frac{\tan{\left(2 x - 2 \right)}}{\sqrt{- x} \sqrt{x + 3}}
- No
tan⁡(2x+2)x3−x=tan⁡(2x−2)−xx+3\frac{\tan{\left(2 x + 2 \right)}}{\sqrt{x} \sqrt{3 - x}} = \frac{\tan{\left(2 x - 2 \right)}}{\sqrt{- x} \sqrt{x + 3}}
- No
es decir, función
no es
par ni impar
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