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Trazado el gráfico de la función/ cot(3*x)*sin(5*x)

Gráfico de la función y = cot(3*x)*sin(5*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cot(3*x)*sin(5*x)
f(x)=sin⁡(5x)cot⁡(3x)f{\left(x \right)} = \sin{\left(5 x \right)} \cot{\left(3 x \right)} 
f = sin(5*x)*cot(3*x)
Gráfico de la función
02468-8-6-4-2-1010-5050
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⁡(5x)cot⁡(3x)=0\sin{\left(5 x \right)} \cot{\left(3 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−7.85398163397448x_{1} = -7.85398163397448
x2=22.6194671058465x_{2} = 22.6194671058465
x3=−31.9395253114962x_{3} = -31.9395253114962
x4=24.5044226980004x_{4} = 24.5044226980004
x5=−25.7610597594363x_{5} = -25.7610597594363
x6=−13.8230076757951x_{6} = -13.8230076757951
x7=62.2035345410779x_{7} = 62.2035345410779
x8=−16.2315620435473x_{8} = -16.2315620435473
x9=−29.845130209103x_{9} = -29.845130209103
x10=47.7522083345649x_{10} = 47.7522083345649
x11=−82.2050077689329x_{11} = -82.2050077689329
x12=25.7610597594363x_{12} = 25.7610597594363
x13=88.4881930761125x_{13} = 88.4881930761125
x14=2.51327412287183x_{14} = 2.51327412287183
x15=30.159289474462x_{15} = 30.159289474462
x16=−93.7241808320955x_{16} = -93.7241808320955
x17=−63.4601716025138x_{17} = -63.4601716025138
x18=86.7079572390783x_{18} = 86.7079572390783
x19=49.6371639267187x_{19} = 49.6371639267187
x20=−84.1946831162065x_{20} = -84.1946831162065
x21=58.1194640914112x_{21} = 58.1194640914112
x22=−73.8274273593601x_{22} = -73.8274273593601
x23=−27.7507351067098x_{23} = -27.7507351067098
x24=76.026542216873x_{24} = 76.026542216873
x25=16.2315620435473x_{25} = 16.2315620435473
x26=10.0530964914873x_{26} = 10.0530964914873
x27=71.6283125018473x_{27} = 71.6283125018473
x28=−64.7168086639497x_{28} = -64.7168086639497
x29=44.6106156809751x_{29} = 44.6106156809751
x30=66.497044500984x_{30} = 66.497044500984
x31=−41.4690230273853x_{31} = -41.4690230273853
x32=−79.7964534011807x_{32} = -79.7964534011807
x33=18.2212373908208x_{33} = 18.2212373908208
x34=−3.76991118430775x_{34} = -3.76991118430775
x35=−40.2123859659494x_{35} = -40.2123859659494
x36=20.4203522483337x_{36} = 20.4203522483337
x37=−86.0796387083603x_{37} = -86.0796387083603
x38=−89.8495498926681x_{38} = -89.8495498926681
x39=3.76991118430775x_{39} = 3.76991118430775
x40=−57.8053048260522x_{40} = -57.8053048260522
x41=−5.75958653158129x_{41} = -5.75958653158129
x42=96.1327351998477x_{42} = 96.1327351998477
x43=40.2123859659494x_{43} = 40.2123859659494
x44=−43.3539786195391x_{44} = -43.3539786195391
x45=−98.0176907920015x_{45} = -98.0176907920015
x46=−100.007366139275x_{46} = -100.007366139275
x47=−67.8584013175395x_{47} = -67.8584013175395
x48=27.7507351067098x_{48} = 27.7507351067098
x49=−56.025068989018x_{49} = -56.025068989018
x50=−60.2138591938044x_{50} = -60.2138591938044
x51=60.2138591938044x_{51} = 60.2138591938044
x52=82.2050077689329x_{52} = 82.2050077689329
x53=−38.2227106186758x_{53} = -38.2227106186758
x54=70.3716754404114x_{54} = 70.3716754404114
x55=80.1106126665397x_{55} = 80.1106126665397
x56=38.2227106186758x_{56} = 38.2227106186758
x57=−18.2212373908208x_{57} = -18.2212373908208
x58=8.16814089933346x_{58} = 8.16814089933346
x59=34.0339204138894x_{59} = 34.0339204138894
x60=−35.8141562509236x_{60} = -35.8141562509236
x61=−78.0162175641465x_{61} = -78.0162175641465
x62=32.0442450666159x_{62} = 32.0442450666159
x63=38.9557489045134x_{63} = 38.9557489045134
x64=−34.0339204138894x_{64} = -34.0339204138894
x65=46.4955712731289x_{65} = 46.4955712731289
x66=−95.8185759344887x_{66} = -95.8185759344887
x67=−69.7433569096934x_{67} = -69.7433569096934
x68=−53.9306738866248x_{68} = -53.9306738866248
x69=−4.71238898038469x_{69} = -4.71238898038469
x70=−71.733032256967x_{70} = -71.733032256967
x71=−11.9380520836412x_{71} = -11.9380520836412
x72=−46.4955712731289x_{72} = -46.4955712731289
x73=74.1415866247191x_{73} = 74.1415866247191
x74=−19.4778744522567x_{74} = -19.4778744522567
x75=92.3628240155399x_{75} = 92.3628240155399
x76=93.6194610769758x_{76} = 93.6194610769758
x77=78.0162175641465x_{77} = 78.0162175641465
x78=54.0353936417444x_{78} = 54.0353936417444
x79=−51.8362787842316x_{79} = -51.8362787842316
x80=98.0176907920015x_{80} = 98.0176907920015
x81=68.4867198482575x_{81} = 68.4867198482575
x82=12.0427718387609x_{82} = 12.0427718387609
x83=−47.7522083345649x_{83} = -47.7522083345649
x84=36.1283155162826x_{84} = 36.1283155162826
x85=−9.94837673636768x_{85} = -9.94837673636768
x86=100.007366139275x_{86} = 100.007366139275
x87=−21.3628300444106x_{87} = -21.3628300444106
x88=−23.5619449019235x_{88} = -23.5619449019235
x89=56.025068989018x_{89} = 56.025068989018
x90=−62.2035345410779x_{90} = -62.2035345410779
x91=−49.7418836818384x_{91} = -49.7418836818384
x92=73.8274273593601x_{92} = 73.8274273593601
x93=14.1371669411541x_{93} = 14.1371669411541
x94=−82.3097275240526x_{94} = -82.3097275240526
x95=−76.026542216873x_{95} = -76.026542216873
x96=90.477868423386x_{96} = 90.477868423386
x97=−91.734505484822x_{97} = -91.734505484822
x98=52.1504380495906x_{98} = 52.1504380495906
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(3*x)*sin(5*x).
sin⁡(0⋅5)cot⁡(0⋅3)\sin{\left(0 \cdot 5 \right)} \cot{\left(0 \cdot 3 \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→−∞(sin⁡(5x)cot⁡(3x))y = \lim_{x \to -\infty}\left(\sin{\left(5 x \right)} \cot{\left(3 x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(sin⁡(5x)cot⁡(3x))y = \lim_{x \to \infty}\left(\sin{\left(5 x \right)} \cot{\left(3 x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cot(3*x)*sin(5*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⁡(5x)cot⁡(3x)x)y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(5 x \right)} \cot{\left(3 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(sin⁡(5x)cot⁡(3x)x)y = x \lim_{x \to \infty}\left(\frac{\sin{\left(5 x \right)} \cot{\left(3 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⁡(5x)cot⁡(3x)=sin⁡(5x)cot⁡(3x)\sin{\left(5 x \right)} \cot{\left(3 x \right)} = \sin{\left(5 x \right)} \cot{\left(3 x \right)}
- Sí
sin⁡(5x)cot⁡(3x)=−sin⁡(5x)cot⁡(3x)\sin{\left(5 x \right)} \cot{\left(3 x \right)} = - \sin{\left(5 x \right)} \cot{\left(3 x \right)}
- No
es decir, función
es
par
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