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y=sin(2pix)-2ctg(x)
Trazado el gráfico de la función/ y=sin(2pix)-2ctg(x)

Gráfico de la función y = y=sin(2pix)-2ctg(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

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

Solución numérica
x1=−70.2265357651359x_{1} = -70.2265357651359
x2=−212.01390462988x_{2} = -212.01390462988
x3=−14.03339517397x_{3} = -14.03339517397
x4=98.9903759183117x_{4} = 98.9903759183117
x5=−64.1050864290982x_{5} = -64.1050864290982
x6=−20.5379725603682x_{6} = -20.5379725603682
x7=86.1023936343095x_{7} = 86.1023936343095
x8=23.4707147217757x_{8} = 23.4707147217757
x9=67.8780288209508x_{9} = 67.8780288209508
x10=102.02468246304x_{10} = 102.02468246304
x11=−102.02468246304x_{11} = -102.02468246304
x12=−80.0268516825209x_{12} = -80.0268516825209
x13=−61.7150553488273x_{13} = -61.7150553488273
x14=61.7150553488273x_{14} = 61.7150553488273
x15=−10.9989313892887x_{15} = -10.9989313892887
x16=39.0673620596802x_{16} = 39.0673620596802
x17=92.9181499607428x_{17} = 92.9181499607428
x18=36.031207550968x_{18} = 36.031207550968
x19=70.2265357651359x_{19} = 70.2265357651359
x20=61.0650086827499x_{20} = 61.0650086827499
x21=23.8838072021773x_{21} = 23.8838072021773
x22=−86.1023936343095x_{22} = -86.1023936343095
x23=−42.1078111544183x_{23} = -42.1078111544183
x24=1.88663734890689x_{24} = 1.88663734890689
x25=−20.1105693500103x_{25} = -20.1105693500103
x26=92.2203029070491x_{26} = 92.2203029070491
x27=7.9644100812265x_{27} = 7.9644100812265
x28=−4.24875363672036x_{28} = -4.24875363672036
x29=−86.5515200661562x_{29} = -86.5515200661562
x30=−32.9967939485838x_{30} = -32.9967939485838
x31=89.48340867786x_{31} = 89.48340867786
x32=95.9555495742604x_{32} = 95.9555495742604
x33=−67.8780288209508x_{33} = -67.8780288209508
x34=−95.9555495742604x_{34} = -95.9555495742604
x35=45.880938354026x_{35} = 45.880938354026
x36=20.1105693500103x_{36} = 20.1105693500103
x37=89.8750764779467x_{37} = 89.8750764779467
x38=14.03339517397x_{38} = 14.03339517397
x39=−17.7418875520688x_{39} = -17.7418875520688
x40=−51.9599971846325x_{40} = -51.9599971846325
x41=−1.88663734890689x_{41} = -1.88663734890689
x42=26.240589246812x_{42} = 26.240589246812
x43=−92.2203029070491x_{43} = -92.2203029070491
x44=17.7418875520688x_{44} = 17.7418875520688
x45=64.1050864290982x_{45} = 64.1050864290982
x46=−58.0290265507479x_{46} = -58.0290265507479
x47=−89.48340867786x_{47} = -89.48340867786
x48=−36.031207550968x_{48} = -36.031207550968
x49=80.0268516825209x_{49} = 80.0268516825209
x50=4.24875363672036x_{50} = 4.24875363672036
x51=−23.8838072021773x_{51} = -23.8838072021773
x52=4.92788185551843x_{52} = 4.92788185551843
x53=76.9925166533029x_{53} = 76.9925166533029
x54=83.0626707591891x_{54} = 83.0626707591891
x55=48.2332532885374x_{55} = 48.2332532885374
x56=−7.9644100812265x_{56} = -7.9644100812265
x57=42.1078111544183x_{57} = 42.1078111544183
x58=−48.2332532885374x_{58} = -48.2332532885374
x59=10.9989313892887x_{59} = 10.9989313892887
x60=−89.8750764779467x_{60} = -89.8750764779467
x61=−26.240589246812x_{61} = -26.240589246812
x62=29.9622077066517x_{62} = 29.9622077066517
x63=58.0290265507479x_{63} = 58.0290265507479
x64=73.9577779870006x_{64} = 73.9577779870006
x65=−45.880938354026x_{65} = -45.880938354026
x66=−39.0673620596802x_{66} = -39.0673620596802
x67=26.3857095119681x_{67} = 26.3857095119681
x68=51.9599971846325x_{68} = 51.9599971846325
x69=−70.4000071799372x_{69} = -70.4000071799372
x70=39.7305761071698x_{70} = 39.7305761071698
x71=−54.9946558497801x_{71} = -54.9946558497801
x72=32.9967939485838x_{72} = 32.9967939485838
x73=−29.9622077066517x_{73} = -29.9622077066517
x74=−39.7305761071698x_{74} = -39.7305761071698
x75=−73.9577779870006x_{75} = -73.9577779870006
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→−∞(sin⁡(2πx)−2cot⁡(x))y = \lim_{x \to -\infty}\left(\sin{\left(2 \pi x \right)} - 2 \cot{\left(x \right)}\right)
True

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

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