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cot(6*x)*tan(2*x)
Trazado el gráfico de la función/ cot(6*x)*tan(2*x)

Gráfico de la función y = cot(6*x)*tan(2*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cot(6*x)*tan(2*x)
f(x)=tan⁡(2x)cot⁡(6x)f{\left(x \right)} = \tan{\left(2 x \right)} \cot{\left(6 x \right)} 
f = tan(2*x)*cot(6*x)
Gráfico de la función
02468-8-6-4-2-1010-100100
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)cot⁡(6x)=0\tan{\left(2 x \right)} \cot{\left(6 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−1.83259571459405x_{1} = -1.83259571459405
x2=−64.1408500107916x_{2} = -64.1408500107916
x3=50.0036830696375x_{3} = 50.0036830696375
x4=−108.123147161049x_{4} = -108.123147161049
x5=26.4417381677141x_{5} = 26.4417381677141
x6=−93.9859802198946x_{6} = -93.9859802198946
x7=31.6777259236971x_{7} = 31.6777259236971
x8=−48.9564855184409x_{8} = -48.9564855184409
x9=−51.5744793964324x_{9} = -51.5744793964324
x10=−15.9697626557481x_{10} = -15.9697626557481
x11=−67.8060414399797x_{11} = -67.8060414399797
x12=−28.012534494509x_{12} = -28.012534494509
x13=68.8532389911763x_{13} = 68.8532389911763
x14=43.720497762458x_{14} = 43.720497762458
x15=−23.8237442897226x_{15} = -23.8237442897226
x16=−6.02138591938044x_{16} = -6.02138591938044
x17=12.30457122656x_{17} = 12.30457122656
x18=87.7027949127151x_{18} = 87.7027949127151
x19=24.8709418409192x_{19} = 24.8709418409192
x20=−95.5567765466895x_{20} = -95.5567765466895
x21=79.8488132787406x_{21} = 79.8488132787406
x22=71.9948316447661x_{22} = 71.9948316447661
x23=−53.6688744988256x_{23} = -53.6688744988256
x24=81.9432083811338x_{24} = 81.9432083811338
x25=98.6983692002793x_{25} = 98.6983692002793
x26=54.7160720500222x_{26} = 54.7160720500222
x27=−89.7971900151083x_{27} = -89.7971900151083
x28=34.2957198016886x_{28} = 34.2957198016886
x29=30.1069295969022x_{29} = 30.1069295969022
x30=−86.1319985859202x_{30} = -86.1319985859202
x31=−79.8488132787406x_{31} = -79.8488132787406
x32=−23.3001455141243x_{32} = -23.3001455141243
x33=20.1585528605345x_{33} = 20.1585528605345
x34=−87.7027949127151x_{34} = -87.7027949127151
x35=−13.8753675533549x_{35} = -13.8753675533549
x36=48.4328867428426x_{36} = 48.4328867428426
x37=−44.2440965380563x_{37} = -44.2440965380563
x38=−81.9432083811338x_{38} = -81.9432083811338
x39=100.269165527074x_{39} = 100.269165527074
x40=8.11578102177363x_{40} = 8.11578102177363
x41=−35.8665161284835x_{41} = -35.8665161284835
x42=59.9520598060052x_{42} = 59.9520598060052
x43=74.0892267471593x_{43} = 74.0892267471593
x44=44.2440965380563x_{44} = 44.2440965380563
x45=−57.857664703612x_{45} = -57.857664703612
x46=42.1497014356631x_{46} = 42.1497014356631
x47=93.9859802198946x_{47} = 93.9859802198946
x48=−59.9520598060052x_{48} = -59.9520598060052
x49=−6.54498469497874x_{49} = -6.54498469497874
x50=315.991861073573x_{50} = 315.991861073573
x51=6.02138591938044x_{51} = 6.02138591938044
x52=15.9697626557481x_{52} = 15.9697626557481
x53=90.8443875663049x_{53} = 90.8443875663049
x54=−97.6511716490827x_{54} = -97.6511716490827
x55=−75.1364242983559x_{55} = -75.1364242983559
x56=−30.1069295969022x_{56} = -30.1069295969022
x57=−105.505153283057x_{57} = -105.505153283057
x58=−21.7293491873294x_{58} = -21.7293491873294
x59=76.7072206251508x_{59} = 76.7072206251508
x60=92.4151838930998x_{60} = 92.4151838930998
x61=17.540558982543x_{61} = 17.540558982543
x62=−73.565627971561x_{62} = -73.565627971561
x63=22.2529479629277x_{63} = 22.2529479629277
x64=66.2352451131848x_{64} = 66.2352451131848
x65=−62.5700536839967x_{65} = -62.5700536839967
x66=−657.901861539263x_{66} = -657.901861539263
x67=−65.7116463375865x_{67} = -65.7116463375865
x68=−75.6600230739542x_{68} = -75.6600230739542
x69=−26.9653369433124x_{69} = -26.9653369433124
x70=52.0980781720307x_{70} = 52.0980781720307
x71=−34.2957198016886x_{71} = -34.2957198016886
x72=56.2868683768171x_{72} = 56.2868683768171
x73=10.7337748997651x_{73} = 10.7337748997651
x74=64.1408500107916x_{74} = 64.1408500107916
x75=−71.9948316447661x_{75} = -71.9948316447661
x76=−9.68657734856853x_{76} = -9.68657734856853
x77=55.2396708256205x_{77} = 55.2396708256205
x78=86.1319985859202x_{78} = 86.1319985859202
x79=96.0803753222878x_{79} = 96.0803753222878
x80=70.4240353179712x_{80} = 70.4240353179712
x81=−77.2308194007491x_{81} = -77.2308194007491
x82=−45.8148928648512x_{82} = -45.8148928648512
x83=−4.45058959258554x_{83} = -4.45058959258554
x84=78.2780169519457x_{84} = 78.2780169519457
x85=−31.6777259236971x_{85} = -31.6777259236971
x86=−37.9609112308767x_{86} = -37.9609112308767
x87=−43.720497762458x_{87} = -43.720497762458
x88=39.5317075576716x_{88} = 39.5317075576716
x89=−350.549380263061x_{89} = -350.549380263061
x90=88.2263936883134x_{90} = 88.2263936883134
x91=28.012534494509x_{91} = 28.012534494509
x92=−50.0036830696375x_{92} = -50.0036830696375
x93=37.9609112308767x_{93} = 37.9609112308767
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 cot(6*x)*tan(2*x).
tan⁡(0⋅2)cot⁡(0⋅6)\tan{\left(0 \cdot 2 \right)} \cot{\left(0 \cdot 6 \right)}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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)cot⁡(6x))y = \lim_{x \to -\infty}\left(\tan{\left(2 x \right)} \cot{\left(6 x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(tan⁡(2x)cot⁡(6x))y = \lim_{x \to \infty}\left(\tan{\left(2 x \right)} \cot{\left(6 x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cot(6*x)*tan(2*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→−∞(tan⁡(2x)cot⁡(6x)x)y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(2 x \right)} \cot{\left(6 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(tan⁡(2x)cot⁡(6x)x)y = x \lim_{x \to \infty}\left(\frac{\tan{\left(2 x \right)} \cot{\left(6 x \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)cot⁡(6x)=tan⁡(2x)cot⁡(6x)\tan{\left(2 x \right)} \cot{\left(6 x \right)} = \tan{\left(2 x \right)} \cot{\left(6 x \right)}
- Sí
tan⁡(2x)cot⁡(6x)=−tan⁡(2x)cot⁡(6x)\tan{\left(2 x \right)} \cot{\left(6 x \right)} = - \tan{\left(2 x \right)} \cot{\left(6 x \right)}
- No
es decir, función
es
par
Gráfico
Gráfico de la función y = cot(6*x)*tan(2*x)
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