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Trazado el gráfico de la función/ cot(2*x)*tan(7*x)

Gráfico de la función y = cot(2*x)*tan(7*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cot(2*x)*tan(7*x)
f(x)=tan⁡(7x)cot⁡(2x)f{\left(x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)} 
f = tan(7*x)*cot(2*x)
Gráfico de la función
02468-8-6-4-2-1010-500500
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⁡(7x)cot⁡(2x)=0\tan{\left(7 x \right)} \cot{\left(2 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−11.7809724509617x_{1} = -11.7809724509617
x2=−38.484510006475x_{2} = -38.484510006475
x3=−89.7597901025655x_{3} = -89.7597901025655
x4=64.6270488738472x_{4} = 64.6270488738472
x5=−49.8166835069239x_{5} = -49.8166835069239
x6=−23.7863443771799x_{6} = -23.7863443771799
x7=36.9137136796801x_{7} = 36.9137136796801
x8=8.0783811092309x_{8} = 8.0783811092309
x9=−31.8647254864108x_{9} = -31.8647254864108
x10=−45.7774929523084x_{10} = -45.7774929523084
x11=2.24399475256414x_{11} = 2.24399475256414
x12=−48.0214877048726x_{12} = -48.0214877048726
x13=12.1175716638463x_{13} = 12.1175716638463
x14=−58.7926625171804x_{14} = -58.7926625171804
x15=−85.7205995479501x_{15} = -85.7205995479501
x16=54.3046730120521x_{16} = 54.3046730120521
x17=−70.0126362800011x_{17} = -70.0126362800011
x18=−46.2262919028212x_{18} = -46.2262919028212
x19=80.3350121417961x_{19} = 80.3350121417961
x20=39.9431065956417x_{20} = 39.9431065956417
x21=−92.0037848551297x_{21} = -92.0037848551297
x22=−62.0464549083984x_{22} = -62.0464549083984
x23=26.030339129744x_{23} = 26.030339129744
x24=−4.03919055461545x_{24} = -4.03919055461545
x25=83.9254037458988x_{25} = 83.9254037458988
x26=−33.7721210260903x_{26} = -33.7721210260903
x27=−13.9127674658977x_{27} = -13.9127674658977
x28=76.2958215871807x_{28} = 76.2958215871807
x29=−52.060678259488x_{29} = -52.060678259488
x30=−97.8381712117964x_{30} = -97.8381712117964
x31=38.1479107935903x_{31} = 38.1479107935903
x32=−17.9519580205131x_{32} = -17.9519580205131
x33=10.322375861795x_{33} = 10.322375861795
x34=52.060678259488x_{34} = 52.060678259488
x35=35.4551170905134x_{35} = 35.4551170905134
x36=96.0429754097451x_{36} = 96.0429754097451
x37=73.1542289335909x_{37} = 73.1542289335909
x38=100.082165964361x_{38} = 100.082165964361
x39=70.0126362800011x_{39} = 70.0126362800011
x40=24.2351433276927x_{40} = 24.2351433276927
x41=20.1959527730772x_{41} = 20.1959527730772
x42=−79.8862131912833x_{42} = -79.8862131912833
x43=68.2174404779498x_{43} = 68.2174404779498
x44=−1.79519580205131x_{44} = -1.79519580205131
x45=8.63937979737193x_{45} = 8.63937979737193
x46=−22.4399475256414x_{46} = -22.4399475256414
x47=21.5423496246157x_{47} = 21.5423496246157
x48=48.0214877048726x_{48} = 48.0214877048726
x49=−71.8078320820524x_{49} = -71.8078320820524
x50=90.2085890530783x_{50} = 90.2085890530783
x51=17.9519580205131x_{51} = 17.9519580205131
x52=−79.4374142407705x_{52} = -79.4374142407705
x53=38.484510006475x_{53} = 38.484510006475
x54=4.03919055461545x_{54} = 4.03919055461545
x55=−9.87357691128221x_{55} = -9.87357691128221
x56=98.2869701623092x_{56} = 98.2869701623092
x57=30.0695296843594x_{57} = 30.0695296843594
x58=−39.9431065956417x_{58} = -39.9431065956417
x59=61.9342551707702x_{59} = 61.9342551707702
x60=−83.9254037458988x_{60} = -83.9254037458988
x61=50.7142814079495x_{61} = 50.7142814079495
x62=34.1087202389749x_{62} = 34.1087202389749
x63=82.1302079438475x_{63} = 82.1302079438475
x64=−55.7632696012188x_{64} = -55.7632696012188
x65=32.3135244369236x_{65} = 32.3135244369236
x66=−63.7294509728215x_{66} = -63.7294509728215
x67=−27.8255349317953x_{67} = -27.8255349317953
x68=−93.798980657181x_{68} = -93.798980657181
x69=78.091017389232x_{69} = 78.091017389232
x70=42.1871013482058x_{70} = 42.1871013482058
x71=−77.7544181763474x_{71} = -77.7544181763474
x72=−53.8558740615393x_{72} = -53.8558740615393
x73=−35.9039160410262x_{73} = -35.9039160410262
x74=−5.83438635666676x_{74} = -5.83438635666676
x75=−74.0518268346165x_{75} = -74.0518268346165
x76=86.1693984984629x_{76} = 86.1693984984629
x77=60.1390593687189x_{77} = 60.1390593687189
x78=92.0037848551297x_{78} = 92.0037848551297
x79=59.2414614676932x_{79} = 59.2414614676932
x80=16.1567622184618x_{80} = 16.1567622184618
x81=−30.0695296843594x_{81} = -30.0695296843594
x82=−65.07584782436x_{82} = -65.07584782436
x83=−75.8470226366679x_{83} = -75.8470226366679
x84=−96.0429754097451x_{84} = -96.0429754097451
x85=−41.738302397693x_{85} = -41.738302397693
x86=−26.030339129744x_{86} = -26.030339129744
x87=−8.0783811092309x_{87} = -8.0783811092309
x88=−87.5157953500014x_{88} = -87.5157953500014
x89=93.4623814442964x_{89} = 93.4623814442964
x90=56.0998688141035x_{90} = 56.0998688141035
x91=46.2262919028212x_{91} = 46.2262919028212
x92=−99.7455667514759x_{92} = -99.7455667514759
x93=−19.7471538225644x_{93} = -19.7471538225644
x94=74.0518268346165x_{94} = 74.0518268346165
x95=−67.768641527437x_{95} = -67.768641527437
x96=64.1782499233343x_{96} = 64.1782499233343
x97=−57.8950646161548x_{97} = -57.8950646161548
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(2*x)*tan(7*x).
tan⁡(0⋅7)cot⁡(0⋅2)\tan{\left(0 \cdot 7 \right)} \cot{\left(0 \cdot 2 \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⁡(7x)cot⁡(2x))y = \lim_{x \to -\infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(tan⁡(7x)cot⁡(2x))y = \lim_{x \to \infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cot(2*x)*tan(7*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⁡(7x)cot⁡(2x)x)y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(tan⁡(7x)cot⁡(2x)x)y = x \lim_{x \to \infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 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⁡(7x)cot⁡(2x)=tan⁡(7x)cot⁡(2x)\tan{\left(7 x \right)} \cot{\left(2 x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)}
- Sí
tan⁡(7x)cot⁡(2x)=−tan⁡(7x)cot⁡(2x)\tan{\left(7 x \right)} \cot{\left(2 x \right)} = - \tan{\left(7 x \right)} \cot{\left(2 x \right)}
- No
es decir, función
es
par
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