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Trazado el gráfico de la función/ cot(x)*cos(3*x)

Gráfico de la función y = cot(x)*cos(3*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cot(x)*cos(3*x)
f(x)=cos⁡(3x)cot⁡(x)f{\left(x \right)} = \cos{\left(3 x \right)} \cot{\left(x \right)} 
f = cos(3*x)*cot(x)
Gráfico de la función
02468-8-6-4-2-1010-10001000
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:
cos⁡(3x)cot⁡(x)=0\cos{\left(3 x \right)} \cot{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π6x_{1} = - \frac{\pi}{6}
x2=π6x_{2} = \frac{\pi}{6}
Solución numérica
x1=84.2994028713261x_{1} = 84.2994028713261
x2=−87.4409955249159x_{2} = -87.4409955249159
x3=92.6769832328586x_{3} = 92.6769832328586
x4=−17.27875947683x_{4} = -17.27875947683
x5=45.553093474491x_{5} = 45.553093474491
x6=−65.4498469497874x_{6} = -65.4498469497874
x7=−1.57079642136732x_{7} = -1.57079642136732
x8=−73.8274272807161x_{8} = -73.8274272807161
x9=95.8185760444286x_{9} = 95.8185760444286
x10=−23.5619449996004x_{10} = -23.5619449996004
x11=−97.9129710368819x_{11} = -97.9129710368819
x12=44.5058959258554x_{12} = 44.5058959258554
x13=−3.66519142918809x_{13} = -3.66519142918809
x14=−67.5442421555971x_{14} = -67.5442421555971
x15=14.1371670789183x_{15} = 14.1371670789183
x16=42.4115007355437x_{16} = 42.4115007355437
x17=−5.75958653158129x_{17} = -5.75958653158129
x18=58.1194643064617x_{18} = 58.1194643064617
x19=−45.5530935776788x_{19} = -45.5530935776788
x20=−25.6563400043166x_{20} = -25.6563400043166
x21=73.8274274664783x_{21} = 73.8274274664783
x22=−14.1371668472527x_{22} = -14.1371668472527
x23=−9.94837673636768x_{23} = -9.94837673636768
x24=−47.6474885794452x_{24} = -47.6474885794452
x25=−7.85398150579211x_{25} = -7.85398150579211
x26=97.9129710368819x_{26} = 97.9129710368819
x27=−39.2699079856935x_{27} = -39.2699079856935
x28=26.7035375819756x_{28} = 26.7035375819756
x29=−21.4675497995303x_{29} = -21.4675497995303
x30=5.75958653158129x_{30} = 5.75958653158129
x31=−86.3937978811637x_{31} = -86.3937978811637
x32=−89.5353907333485x_{32} = -89.5353907333485
x33=−61.2610564810276x_{33} = -61.2610564810276
x34=−82.2050077689329x_{34} = -82.2050077689329
x35=66.497044500984x_{35} = 66.497044500984
x36=−20.4203521884053x_{36} = -20.4203521884053
x37=−16.2315620435473x_{37} = -16.2315620435473
x38=−93.7241808320955x_{38} = -93.7241808320955
x39=75.9218224617533x_{39} = 75.9218224617533
x40=−36.1283154261792x_{40} = -36.1283154261792
x41=12.0427718387609x_{41} = 12.0427718387609
x42=48.6946861261374x_{42} = 48.6946861261374
x43=−34.0339204138894x_{43} = -34.0339204138894
x44=86.3937978930241x_{44} = 86.3937978930241
x45=80.1106131571704x_{45} = 80.1106131571704
x46=82.2050077689329x_{46} = 82.2050077689329
x47=9.94837673636768x_{47} = 9.94837673636768
x48=−51.8362786912223x_{48} = -51.8362786912223
x49=60.2138591938044x_{49} = 60.2138591938044
x50=−80.110612584662x_{50} = -80.110612584662
x51=31.9395253114962x_{51} = 31.9395253114962
x52=−49.7418836818384x_{52} = -49.7418836818384
x53=29.8451303100012x_{53} = 29.8451303100012
x54=100.007366139275x_{54} = 100.007366139275
x55=−42.4115007503822x_{55} = -42.4115007503822
x56=49.7418836818384x_{56} = 49.7418836818384
x57=78.0162175641465x_{57} = 78.0162175641465
x58=38.2227106186758x_{58} = 38.2227106186758
x59=−91.6297857297023x_{59} = -91.6297857297023
x60=7.85398173147262x_{60} = 7.85398173147262
x61=64.4026493142142x_{61} = 64.4026493142142
x62=53.9306738866248x_{62} = 53.9306738866248
x63=−95.818575868398x_{63} = -95.818575868398
x64=27.7507351067098x_{64} = 27.7507351067098
x65=−31.9395253114962x_{65} = -31.9395253114962
x66=−56.025068989018x_{66} = -56.025068989018
x67=71.733032256967x_{67} = 71.733032256967
x68=23.5619449251568x_{68} = 23.5619449251568
x69=1.57079637042477x_{69} = 1.57079637042477
x70=−53.9306738866248x_{70} = -53.9306738866248
x71=−69.6386371545737x_{71} = -69.6386371545737
x72=−60.2138591938044x_{72} = -60.2138591938044
x73=16.2315620435473x_{73} = 16.2315620435473
x74=−78.0162175641465x_{74} = -78.0162175641465
x75=−75.9218224617533x_{75} = -75.9218224617533
x76=67.5442420166601x_{76} = 67.5442420166601
x77=−12.0427718387609x_{77} = -12.0427718387609
x78=56.025068989018x_{78} = 56.025068989018
x79=40.317105721069x_{79} = 40.317105721069
x80=−64.4026493148073x_{80} = -64.4026493148073
x81=51.836278888336x_{81} = 51.836278888336
x82=−38.2227106186758x_{82} = -38.2227106186758
x83=−58.1194640053129x_{83} = -58.1194640053129
x84=4.71238904670105x_{84} = 4.71238904670105
x85=−100.007366139275x_{85} = -100.007366139275
x86=36.1283159857265x_{86} = 36.1283159857265
x87=−71.733032256967x_{87} = -71.733032256967
x88=−27.7507351067098x_{88} = -27.7507351067098
x89=22.5147473507269x_{89} = 22.5147473507269
x90=70.6858346769734x_{90} = 70.6858346769734
x91=−83.252205000398x_{91} = -83.252205000398
x92=89.5353905493254x_{92} = 89.5353905493254
x93=34.0339204138894x_{93} = 34.0339204138894
x94=−29.845130099496x_{94} = -29.845130099496
x95=18.3259571459405x_{95} = 18.3259571459405
x96=−43.4586983746588x_{96} = -43.4586983746588
x97=20.4203521570154x_{97} = 20.4203521570154
x98=93.7241808320955x_{98} = 93.7241808320955
x99=62.3082542961976x_{99} = 62.3082542961976
x100=88.4881930761125x_{100} = 88.4881930761125
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(x)*cos(3*x).
cos⁡(0⋅3)cot⁡(0)\cos{\left(0 \cdot 3 \right)} \cot{\left(0 \right)}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
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→−∞(cos⁡(3x)cot⁡(x))y = \lim_{x \to -\infty}\left(\cos{\left(3 x \right)} \cot{\left(x \right)}\right)
True

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

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