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Trazado el gráfico de la función/ tg2x-ctg3x+1

Gráfico de la función y = tg2x-ctg3x+1

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = tan(2*x) - cot(3*x) + 1
f(x)=(tan⁡(2x)−cot⁡(3x))+1f{\left(x \right)} = \left(\tan{\left(2 x \right)} - \cot{\left(3 x \right)}\right) + 1 
f = tan(2*x) - cot(3*x) + 1
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⁡(2x)−cot⁡(3x))+1=0\left(\tan{\left(2 x \right)} - \cot{\left(3 x \right)}\right) + 1 = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−56.3453251074414x_{1} = -56.3453251074414
x2=−14.3209455143941x_{2} = -14.3209455143941
x3=−18.6462132643639x_{3} = -18.6462132643639
x4=−100.327622257699x_{4} = -100.327622257699
x5=−41.2863931096546x_{5} = -41.2863931096546
x6=15.9113059251238x_{6} = 15.9113059251238
x7=−12.3630279571843x_{7} = -12.3630279571843
x8=−80.2943912397797x_{8} = -80.2943912397797
x9=91.3095296112788x_{9} = 91.3095296112788
x10=81.8847516505095x_{10} = 81.8847516505095
x11=−16.1536518809363x_{11} = -16.1536518809363
x12=93.8020909947065x_{12} = 93.8020909947065
x13=78.0941277267575x_{13} = 78.0941277267575
x14=2.69590404060247x_{14} = 2.69590404060247
x15=3.34493531076463x_{15} = 3.34493531076463
x16=−23.7457234751634x_{16} = -23.7457234751634
x17=7.67020306073449x_{17} = 7.67020306073449
x18=−30.028908782343x_{18} = -30.028908782343
x19=22.1944912323034x_{19} = 22.1944912323034
x20=51.6525002109916x_{20} = 51.6525002109916
x21=68.6693497659881x_{21} = 68.6693497659881
x22=−58.3032426646512x_{22} = -58.3032426646512
x23=75.6015663433299x_{23} = 75.6015663433299
x24=−53.8527637240138x_{24} = -53.8527637240138
x25=−74.0112059326001x_{25} = -74.0112059326001
x26=−31.8616151488853x_{26} = -31.8616151488853
x27=−63.7920330422437x_{27} = -63.7920330422437
x28=57.9356855181712x_{28} = 57.9356855181712
x29=49.8197938444494x_{29} = 49.8197938444494
x30=−91.5518755670913x_{30} = -91.5518755670913
x31=−19.2952445345261x_{31} = -19.2952445345261
x32=66.1767883825605x_{32} = 66.1767883825605
x33=−25.5784298417057x_{33} = -25.5784298417057
x34=88.1679369576891x_{34} = 88.1679369576891
x35=37.9024545002524x_{35} = 37.9024545002524
x36=12.1206820013719x_{36} = 12.1206820013719
x37=−8.03776020721448x_{37} = -8.03776020721448
x38=−82.1270976063219x_{38} = -82.1270976063219
x39=−85.7831816173722x_{39} = -85.7831816173722
x40=−45.736872050292x_{40} = -45.736872050292
x41=−6.07984265000475x_{41} = -6.07984265000475
x42=−9.8704665737567x_{42} = -9.8704665737567
x43=13.9533883679141x_{43} = 13.9533883679141
x44=−78.33647368257x_{44} = -78.33647368257
x45=98.3120291517831x_{45} = 98.3120291517831
x46=−50.0621398002619x_{46} = -50.0621398002619
x47=−36.3120940895226x_{47} = -36.3120940895226
x48=−87.7612516433394x_{48} = -87.7612516433394
x49=−89.7191692005491x_{49} = -89.7191692005491
x50=31.6192691930728x_{50} = 31.6192691930728
x51=−3.58728126657711x_{51} = -3.58728126657711
x52=84.3773130339371x_{52} = 84.3773130339371
x53=42.2277222502222x_{53} = 42.2277222502222
x54=44.1856398074319x_{54} = 44.1856398074319
x55=18.4038673085514x_{55} = 18.4038673085514
x56=25.3360838858932x_{56} = 25.3360838858932
x57=−94.044436950519x_{57} = -94.044436950519
x58=71.8109424195779x_{58} = 71.8109424195779
x59=53.6104177682013x_{59} = 53.6104177682013
x60=−96.0023545077287x_{60} = -96.0023545077287
x61=62.3861644588085x_{61} = 62.3861644588085
x62=−72.0532883753904x_{62} = -72.0532883753904
x63=79.9268340932997x_{63} = 79.9268340932997
x64=29.661351635863x_{64} = 29.661351635863
x65=95.6347973612487x_{65} = 95.6347973612487
x66=56.102979151629x_{66} = 56.102979151629
x67=86.2100194004793x_{67} = 86.2100194004793
x68=35.9445369430426x_{68} = 35.9445369430426
x69=−28.0709912251333x_{69} = -28.0709912251333
x70=−34.3541765323129x_{70} = -34.3541765323129
x71=−67.7280206254206x_{71} = -67.7280206254206
x72=−21.7878059179537x_{72} = -21.7878059179537
x73=−1.75457490003489x_{73} = -1.75457490003489
x74=24.687052615731x_{74} = 24.687052615731
x75=47.3272324610217x_{75} = 47.3272324610217
x76=100.085276301886x_{76} = 100.085276301886
x77=9.62812061794421x_{77} = 9.62812061794421
x78=−75.8439122991424x_{78} = -75.8439122991424
x79=−47.5695784168342x_{79} = -47.5695784168342
x80=−97.8350608742709x_{80} = -97.8350608742709
x81=20.2365736750937x_{81} = 20.2365736750937
x82=−85.2686902599117x_{82} = -85.2686902599117
x83=40.39501588368x_{83} = 40.39501588368
x84=−43.7789544930823x_{84} = -43.7789544930823
x85=27.8286452693208x_{85} = 27.8286452693208
x86=−60.1359490311934x_{86} = -60.1359490311934
x87=70.0376952694749x_{87} = 70.0376952694749
x88=−38.1448004560648x_{88} = -38.1448004560648
x89=73.6436487861201x_{89} = 73.6436487861201
x90=−69.5607269919628x_{90} = -69.5607269919628
x91=34.1118305765004x_{91} = 34.1118305765004
x92=5.83749669419227x_{92} = 5.83749669419227
x93=64.2188708253508x_{93} = 64.2188708253508
x94=−52.0200573574716x_{94} = -52.0200573574716
x95=59.8936030753809x_{95} = 59.8936030753809
x96=−65.7701030682108x_{96} = -65.7701030682108
x97=−63.2775416847832x_{97} = -63.2775416847832
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
2tan⁡2(2x)+3cot⁡2(3x)+5=02 \tan^{2}{\left(2 x \right)} + 3 \cot^{2}{\left(3 x \right)} + 5 = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga extremos
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⁡(3x))+1)y = \lim_{x \to -\infty}\left(\left(\tan{\left(2 x \right)} - \cot{\left(3 x \right)}\right) + 1\right)
True

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

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