Sr Examen

Otras calculadoras

  • ¿Cómo usar?

  • Gráfico de la función y =:
  • x^2*e^(2-x) x^2*e^(2-x)
  • x^3-12*x+5 x^3-12*x+5
  • x^2-9*x+14 x^2-9*x+14
  • -x^2+6*x-4 -x^2+6*x-4

  • Expresiones idénticas

  • sin(ocho *x)/((cot(tres *x)*tan(cinco *x)^ dos))
  • seno de (8 multiplicar por x) dividir por (( cotangente de (3 multiplicar por x) multiplicar por tangente de (5 multiplicar por x) al cuadrado ))
  • seno de (ocho multiplicar por x) dividir por (( cotangente de (tres multiplicar por x) multiplicar por tangente de (cinco multiplicar por x) en el grado dos))
  • sin(8*x)/((cot(3*x)*tan(5*x)2))
  • sin8*x/cot3*x*tan5*x2
  • sin(8*x)/((cot(3*x)*tan(5*x)²))
  • sin(8*x)/((cot(3*x)*tan(5*x) en el grado 2))
  • sin(8x)/((cot(3x)tan(5x)^2))
  • sin(8x)/((cot(3x)tan(5x)2))
  • sin8x/cot3xtan5x2
  • sin8x/cot3xtan5x^2
  • sin(8*x) dividir por ((cot(3*x)*tan(5*x)^2))

  • Expresiones con funciones

  • Seno sin
  • sin(-x-(pi/3))+1
  • sin(x+2)/(x^2-6*x-16)
  • sin(x)*e^((1/2)*cot(x)^(2))
  • sin(x)+log(sin(x))
  • sin(a)*cos(a)
Trazado el gráfico de la función/ sin(8*x)/((cot(3*x)*tan(5*x)^2))

Gráfico de la función y = sin(8*x)/((cot(3*x)*tan(5*x)^2))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
            sin(8*x)     
f(x) = ------------------
                   2     
       cot(3*x)*tan (5*x)
f(x)=sin⁡(8x)tan⁡2(5x)cot⁡(3x)f{\left(x \right)} = \frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} 
f = sin(8*x)/((tan(5*x)^2*cot(3*x)))
Gráfico de la función
02468-8-6-4-2-1010-250000250000
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
x2=0.523598775598299x_{2} = 0.523598775598299
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⁡(8x)tan⁡2(5x)cot⁡(3x)=0\frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=π8x_{1} = \frac{\pi}{8}
Solución numérica
x1=4.0840704606004x_{1} = 4.0840704606004
x2=−43.6681379206901x_{2} = -43.6681379206901
x3=81.9955682638974x_{3} = 81.9955682638974
x4=54.3495528530231x_{4} = 54.3495528530231
x5=79.5870138909414x_{5} = 79.5870138909414
x6=−85.7654794540767x_{6} = -85.7654794540767
x7=−83.7758040957278x_{7} = -83.7758040957278
x8=−92.0486646786617x_{8} = -92.0486646786617
x9=90.1637091431017x_{9} = 90.1637091431017
x10=−65.6592864924134x_{10} = -65.6592864924134
x11=26.0752190201569x_{11} = 26.0752190201569
x12=68.172560583868x_{12} = 68.172560583868
x13=−23.9546439836222x_{13} = -23.9546439836222
x14=70.0575161516737x_{14} = 70.0575161516737
x15=93.9336203825052x_{15} = 93.9336203825052
x16=−93.9336204254789x_{16} = -93.9336204254789
x17=61.889375228658x_{17} = 61.889375228658
x18=24.1902634542764x_{18} = 24.1902634542764
x19=−16.0221225106729x_{19} = -16.0221225106729
x20=32.3584043293622x_{20} = 32.3584043293622
x21=−26.075218919614x_{21} = -26.075218919614
x22=5.96902607091754x_{22} = 5.96902607091754
x23=48.0663675835174x_{23} = 48.0663675835174
x24=98.3318499899683x_{24} = 98.3318499899683
x25=−4.08407034014021x_{25} = -4.08407034014021
x26=2.19911488207896x_{26} = 2.19911488207896
x27=39.8982267758535x_{27} = 39.8982267758535
x28=76.3407014159574x_{28} = 76.3407014159574
x29=56.8628270273554x_{29} = 56.8628270273554
x30=−51.8362786815231x_{30} = -51.8362786815231
x31=−95.8185758680245x_{31} = -95.8185758680245
x32=−97.703531526049x_{32} = -97.703531526049
x33=−48.0663675037548x_{33} = -48.0663675037548
x34=−73.8274272777072x_{34} = -73.8274272777072
x35=−55.7632696012188x_{35} = -55.7632696012188
x36=84.5088423324891x_{36} = 84.5088423324891
x37=−70.0575160904909x_{37} = -70.0575160904909
x38=−68.0678408277789x_{38} = -68.0678408277789
x39=−1.96349540849362x_{39} = -1.96349540849362
x40=60.0044196781483x_{40} = 60.0044196781483
x41=78.2256570938239x_{41} = 78.2256570938239
x42=30.2378292908018x_{42} = 30.2378292908018
x43=−19.7920336938887x_{43} = -19.7920336938887
x44=64.009950316892x_{44} = 64.009950316892
x45=−53.7212343925829x_{45} = -53.7212343925829
x46=10.3672558026092x_{46} = 10.3672558026092
x47=−31.7300858140222x_{47} = -31.7300858140222
x48=16.0221225047861x_{48} = 16.0221225047861
x49=−77.7544181763474x_{49} = -77.7544181763474
x50=20.0276531666349x_{50} = 20.0276531666349
x51=−80.110612703956x_{51} = -80.110612703956
x52=71.9424718067689x_{52} = 71.9424718067689
x53=74.2201264410589x_{53} = 74.2201264410589
x54=−87.6504350605101x_{54} = -87.6504350605101
x55=−46.1814119414824x_{55} = -46.1814119414824
x56=22.3053078070749x_{56} = 22.3053078070749
x57=38.0132710916724x_{57} = 38.0132710916724
x58=−38.0132710937965x_{58} = -38.0132710937965
x59=56.2345085114092x_{59} = 56.2345085114092
x60=−13.7444678594553x_{60} = -13.7444678594553
x61=12.2522113473755x_{61} = 12.2522113473755
x62=14.7654854459781x_{62} = 14.7654854459781
x63=−81.9955682641137x_{63} = -81.9955682641137
x64=−90.0589894029074x_{64} = -90.0589894029074
x65=49.9513232295974x_{65} = 49.9513232295974
x66=8.24668071567321x_{66} = 8.24668071567321
x67=−61.7846555205993x_{67} = -61.7846555205993
x68=92.0486647239583x_{68} = 92.0486647239583
x69=−60.0044196783785x_{69} = -60.0044196783785
x70=46.1814120216464x_{70} = 46.1814120216464
x71=44.2964563856823x_{71} = 44.2964563856823
x72=−99.7455667514759x_{72} = -99.7455667514759
x73=−33.7721210260903x_{73} = -33.7721210260903
x74=17.9070782300193x_{74} = 17.9070782300193
x75=−49.9513232555573x_{75} = -49.9513232555573
x76=66.2876049652275x_{76} = 66.2876049652275
x77=−39.8982266801284x_{77} = -39.8982266801284
x78=34.2433599291993x_{78} = 34.2433599291993
x79=−9.73893723381938x_{79} = -9.73893723381938
x80=−63.7743308534719x_{80} = -63.7743308534719
x81=86.0010988920206x_{81} = 86.0010988920206
x82=100.216805676295x_{82} = 100.216805676295
x83=−75.7123829677639x_{83} = -75.7123829677639
x84=42.0188017417635x_{84} = 42.0188017417635
x85=88.278753545553x_{85} = 88.278753545553
x86=−27.9601746691207x_{86} = -27.9601746691207
x87=−5.96902608223638x_{87} = -5.96902608223638
x88=−21.6769893464598x_{88} = -21.6769893464598
x89=52.2289778659303x_{89} = 52.2289778659303
x90=−17.9070781008954x_{90} = -17.9070781008954
x91=−59.3761011436045x_{91} = -59.3761011436045
x92=27.9601746509926x_{92} = 27.9601746509926
x93=−71.9424718411691x_{93} = -71.9424718411691
x94=−41.7831822726009x_{94} = -41.7831822726009
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 sin(8*x)/((cot(3*x)*tan(5*x)^2)).
sin⁡(0⋅8)tan⁡2(0⋅5)cot⁡(0⋅3)\frac{\sin{\left(0 \cdot 8 \right)}}{\tan^{2}{\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 verticales
Hay:
x1=0x_{1} = 0
x2=0.523598775598299x_{2} = 0.523598775598299
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⁡(8x)tan⁡2(5x)cot⁡(3x))y = \lim_{x \to -\infty}\left(\frac{\sin{\left(8 x \right)}}{\tan^{2}{\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⁡(8x)tan⁡2(5x)cot⁡(3x))y = \lim_{x \to \infty}\left(\frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(8*x)/((cot(3*x)*tan(5*x)^2)), 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→−∞(1tan⁡2(5x)cot⁡(3x)sin⁡(8x)x)y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} \sin{\left(8 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(1tan⁡2(5x)cot⁡(3x)sin⁡(8x)x)y = x \lim_{x \to \infty}\left(\frac{\frac{1}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} \sin{\left(8 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⁡(8x)tan⁡2(5x)cot⁡(3x)=sin⁡(8x)tan⁡2(5x)cot⁡(3x)\frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} = \frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}}
- No
sin⁡(8x)tan⁡2(5x)cot⁡(3x)=−sin⁡(8x)tan⁡2(5x)cot⁡(3x)\frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} = - \frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор