Sr Examen

Otras calculadoras

tan(2*x)/((2*x^2))

  • ¿Cómo usar?

  • Gráfico de la función y =:
  • 5-x 5-x
  • (1-x^3)/x^2 (1-x^3)/x^2
  • x/(x^2-5) x/(x^2-5)
  • 3*x-x^3 3*x-x^3

  • Expresiones idénticas

  • tan(dos *x)/((dos *x^ dos))
  • tangente de (2 multiplicar por x) dividir por ((2 multiplicar por x al cuadrado ))
  • tangente de (dos multiplicar por x) dividir por ((dos multiplicar por x en el grado dos))
  • tan(2*x)/((2*x2))
  • tan2*x/2*x2
  • tan(2*x)/((2*x²))
  • tan(2*x)/((2*x en el grado 2))
  • tan(2x)/((2x^2))
  • tan(2x)/((2x2))
  • tan2x/2x2
  • tan2x/2x^2
  • tan(2*x) dividir por ((2*x^2))

  • Expresiones con funciones

  • Tangente tan
  • tan(pi/3-2*x)
  • tan(x+pi/4)-2
  • tan(3)^2/((10*x))
  • tan(tan(2*x))
  • tan(11*x/20+1/10)
Trazado el gráfico de la función/ tan(2*x)/((2*x^2))

Gráfico de la función y = tan(2*x)/((2*x^2))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       tan(2*x)
f(x) = --------
            2  
         2*x
f(x)=tan⁡(2x)2x2f{\left(x \right)} = \frac{\tan{\left(2 x \right)}}{2 x^{2}} 
f = tan(2*x)/((2*x^2))
Gráfico de la función
02468-8-6-4-2-1010-5050
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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)2x2=0\frac{\tan{\left(2 x \right)}}{2 x^{2}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=65.9734457253857x_{1} = 65.9734457253857
x2=−64.4026493985908x_{2} = -64.4026493985908
x3=−23.5619449019235x_{3} = -23.5619449019235
x4=−29.845130209103x_{4} = -29.845130209103
x5=−21.9911485751286x_{5} = -21.9911485751286
x6=21.9911485751286x_{6} = 21.9911485751286
x7=−3.14159265358979x_{7} = -3.14159265358979
x8=1.5707963267949x_{8} = 1.5707963267949
x9=−15.707963267949x_{9} = -15.707963267949
x10=42.4115008234622x_{10} = 42.4115008234622
x11=4.71238898038469x_{11} = 4.71238898038469
x12=9.42477796076938x_{12} = 9.42477796076938
x13=97.3893722612836x_{13} = 97.3893722612836
x14=36.1283155162826x_{14} = 36.1283155162826
x15=53.4070751110265x_{15} = 53.4070751110265
x16=23.5619449019235x_{16} = 23.5619449019235
x17=6.28318530717959x_{17} = 6.28318530717959
x18=−17.2787595947439x_{18} = -17.2787595947439
x19=26.7035375555132x_{19} = 26.7035375555132
x20=−34.5575191894877x_{20} = -34.5575191894877
x21=−80.1106126665397x_{21} = -80.1106126665397
x22=86.3937979737193x_{22} = 86.3937979737193
x23=64.4026493985908x_{23} = 64.4026493985908
x24=−83.2522053201295x_{24} = -83.2522053201295
x25=−95.8185759344887x_{25} = -95.8185759344887
x26=28.2743338823081x_{26} = 28.2743338823081
x27=−94.2477796076938x_{27} = -94.2477796076938
x28=−12.5663706143592x_{28} = -12.5663706143592
x29=−1.5707963267949x_{29} = -1.5707963267949
x30=−86.3937979737193x_{30} = -86.3937979737193
x31=−25.1327412287183x_{31} = -25.1327412287183
x32=73.8274273593601x_{32} = 73.8274273593601
x33=−53.4070751110265x_{33} = -53.4070751110265
x34=−39.2699081698724x_{34} = -39.2699081698724
x35=84.8230016469244x_{35} = 84.8230016469244
x36=67.5442420521806x_{36} = 67.5442420521806
x37=70.6858347057703x_{37} = 70.6858347057703
x38=59.6902604182061x_{38} = 59.6902604182061
x39=56.5486677646163x_{39} = 56.5486677646163
x40=−42.4115008234622x_{40} = -42.4115008234622
x41=72.2566310325652x_{41} = 72.2566310325652
x42=−50.2654824574367x_{42} = -50.2654824574367
x43=−51.8362787842316x_{43} = -51.8362787842316
x44=58.1194640914112x_{44} = 58.1194640914112
x45=−73.8274273593601x_{45} = -73.8274273593601
x46=51.8362787842316x_{46} = 51.8362787842316
x47=78.5398163397448x_{47} = 78.5398163397448
x48=−87.9645943005142x_{48} = -87.9645943005142
x49=37.6991118430775x_{49} = 37.6991118430775
x50=−6.28318530717959x_{50} = -6.28318530717959
x51=−20.4203522483337x_{51} = -20.4203522483337
x52=−37.6991118430775x_{52} = -37.6991118430775
x53=−43.9822971502571x_{53} = -43.9822971502571
x54=29.845130209103x_{54} = 29.845130209103
x55=−45.553093477052x_{55} = -45.553093477052
x56=80.1106126665397x_{56} = 80.1106126665397
x57=−58.1194640914112x_{57} = -58.1194640914112
x58=−100.530964914873x_{58} = -100.530964914873
x59=−36.1283155162826x_{59} = -36.1283155162826
x60=−72.2566310325652x_{60} = -72.2566310325652
x61=−81.6814089933346x_{61} = -81.6814089933346
x62=−65.9734457253857x_{62} = -65.9734457253857
x63=−28.2743338823081x_{63} = -28.2743338823081
x64=−56.5486677646163x_{64} = -56.5486677646163
x65=−67.5442420521806x_{65} = -67.5442420521806
x66=31.4159265358979x_{66} = 31.4159265358979
x67=43.9822971502571x_{67} = 43.9822971502571
x68=−47.1238898038469x_{68} = -47.1238898038469
x69=100.530964914873x_{69} = 100.530964914873
x70=−7.85398163397448x_{70} = -7.85398163397448
x71=48.6946861306418x_{71} = 48.6946861306418
x72=−97.3893722612836x_{72} = -97.3893722612836
x73=89.5353906273091x_{73} = 89.5353906273091
x74=81.6814089933346x_{74} = 81.6814089933346
x75=−75.398223686155x_{75} = -75.398223686155
x76=−78.5398163397448x_{76} = -78.5398163397448
x77=7.85398163397448x_{77} = 7.85398163397448
x78=−14.1371669411541x_{78} = -14.1371669411541
x79=50.2654824574367x_{79} = 50.2654824574367
x80=94.2477796076938x_{80} = 94.2477796076938
x81=−91.106186954104x_{81} = -91.106186954104
x82=−59.6902604182061x_{82} = -59.6902604182061
x83=12.5663706143592x_{83} = 12.5663706143592
x84=−69.1150383789755x_{84} = -69.1150383789755
x85=14.1371669411541x_{85} = 14.1371669411541
x86=18.8495559215388x_{86} = 18.8495559215388
x87=34.5575191894877x_{87} = 34.5575191894877
x88=20.4203522483337x_{88} = 20.4203522483337
x89=45.553093477052x_{89} = 45.553093477052
x90=95.8185759344887x_{90} = 95.8185759344887
x91=15.707963267949x_{91} = 15.707963267949
x92=−89.5353906273091x_{92} = -89.5353906273091
x93=87.9645943005142x_{93} = 87.9645943005142
x94=92.6769832808989x_{94} = 92.6769832808989
x95=40.8407044966673x_{95} = 40.8407044966673
x96=−9.42477796076938x_{96} = -9.42477796076938
x97=62.8318530717959x_{97} = 62.8318530717959
x98=−31.4159265358979x_{98} = -31.4159265358979
x99=−61.261056745001x_{99} = -61.261056745001
x100=75.398223686155x_{100} = 75.398223686155
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 tan(2*x)/((2*x^2)).
tan⁡(0⋅2)2⋅02\frac{\tan{\left(0 \cdot 2 \right)}}{2 \cdot 0^{2}}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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
12x2(2tan⁡2(2x)+2)−tan⁡(2x)x3=0\frac{1}{2 x^{2}} \left(2 \tan^{2}{\left(2 x \right)} + 2\right) - \frac{\tan{\left(2 x \right)}}{x^{3}} = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga extremos
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
4(tan⁡2(2x)+1)tan⁡(2x)−4(tan⁡2(2x)+1)x+3tan⁡(2x)x2x2=0\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} + \frac{3 \tan{\left(2 x \right)}}{x^{2}}}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=56.5575053321614x_{1} = 56.5575053321614
x2=−7.91608708649368x_{2} = -7.91608708649368
x3=50.2754234155367x_{3} = 50.2754234155367
x4=−28.2919828766378x_{4} = -28.2919828766378
x5=−75.4048532961614x_{5} = -75.4048532961614
x6=−43.993656070588x_{6} = -43.993656070588
x7=−95.8237932297513x_{7} = -95.8237932297513
x8=84.8288949778237x_{8} = 84.8288949778237
x9=−58.1280630324907x_{9} = -58.1280630324907
x10=22.013811032214x_{10} = 22.013811032214
x11=36.142138328462x_{11} = 36.142138328462
x12=−80.1168524977756x_{12} = -80.1168524977756
x13=−6.35980029715572x_{13} = -6.35980029715572
x14=59.698633274931x_{14} = 59.698633274931
x15=−31.431816577959x_{15} = -31.431816577959
x16=23.5831053765957x_{16} = 23.5831053765957
x17=−51.8459188611063x_{17} = -51.8459188611063
x18=86.3995841990004x_{18} = 86.3995841990004
x19=78.5461809042149x_{19} = 78.5461809042149
x20=42.4232797189588x_{20} = 42.4232797189588
x21=70.6929060186589x_{21} = 70.6929060186589
x22=75.4048532961614x_{22} = 75.4048532961614
x23=9.47691570368212x_{23} = 9.47691570368212
x24=−39.2826275190208x_{24} = -39.2826275190208
x25=40.8529355847239x_{25} = 40.8529355847239
x26=94.253083827148x_{26} = 94.253083827148
x27=15.7395925335903x_{27} = 15.7395925335903
x28=−1.7899510180818x_{28} = -1.7899510180818
x29=72.2635487154488x_{29} = 72.2635487154488
x30=29.8618536848212x_{30} = 29.8618536848212
x31=81.687528885288x_{31} = 81.687528885288
x32=−14.1722587949072x_{32} = -14.1722587949072
x33=95.8237932297513x_{33} = 95.8237932297513
x34=−61.2692150963965x_{34} = -61.2692150963965
x35=51.8459188611063x_{35} = 51.8459188611063
x36=−72.2635487154488x_{36} = -72.2635487154488
x37=26.7222202716231x_{37} = 26.7222202716231
x38=67.5516420403464x_{38} = 67.5516420403464
x39=28.2919828766378x_{39} = 28.2919828766378
x40=−53.4164319752475x_{40} = -53.4164319752475
x41=−65.9810217771819x_{41} = -65.9810217771819
x42=−20.4447453397051x_{42} = -20.4447453397051
x43=−22.013811032214x_{43} = -22.013811032214
x44=−47.1344925787985x_{44} = -47.1344925787985
x45=−73.8341979438688x_{45} = -73.8341979438688
x46=−34.5719686876018x_{46} = -34.5719686876018
x47=−42.4232797189588x_{47} = -42.4232797189588
x48=97.3945054349341x_{48} = 97.3945054349341
x49=89.5409739087494x_{49} = 89.5409739087494
x50=92.6823773695257x_{50} = 92.6823773695257
x51=45.5640613174892x_{51} = 45.5640613174892
x52=14.1722587949072x_{52} = 14.1722587949072
x53=−50.2754234155367x_{53} = -50.2754234155367
x54=73.8341979438688x_{54} = 73.8341979438688
x55=80.1168524977756x_{55} = 80.1168524977756
x56=−56.5575053321614x_{56} = -56.5575053321614
x57=53.4164319752475x_{57} = 53.4164319752475
x58=−25.1525859727656x_{58} = -25.1525859727656
x59=−69.1222702982671x_{59} = -69.1222702982671
x60=−9.47691570368212x_{60} = -9.47691570368212
x61=48.7049473440497x_{61} = 48.7049473440497
x62=37.7123600115464x_{62} = 37.7123600115464
x63=20.4447453397051x_{63} = 20.4447453397051
x64=−94.253083827148x_{64} = -94.253083827148
x65=−64.4104100928947x_{65} = -64.4104100928947
x66=−15.7395925335903x_{66} = -15.7395925335903
x67=4.81183048104258x_{67} = 4.81183048104258
x68=18.8759645638955x_{68} = 18.8759645638955
x69=7.91608708649368x_{69} = 7.91608708649368
x70=64.4104100928947x_{70} = 64.4104100928947
x71=58.1280630324907x_{71} = 58.1280630324907
x72=−78.5461809042149x_{72} = -78.5461809042149
x73=−12.6057680793701x_{73} = -12.6057680793701
x74=−91.111674009098x_{74} = -91.111674009098
x75=−59.698633274931x_{75} = -59.698633274931
x76=65.9810217771819x_{76} = 65.9810217771819
x77=−100.535937727896x_{77} = -100.535937727896
x78=1.7899510180818x_{78} = 1.7899510180818
x79=−36.142138328462x_{79} = -36.142138328462
x80=87.9702772429881x_{80} = 87.9702772429881
x81=−86.3995841990004x_{81} = -86.3995841990004
x82=−37.7123600115464x_{82} = -37.7123600115464
x83=62.8398076299066x_{83} = 62.8398076299066
x84=6.35980029715572x_{84} = 6.35980029715572
x85=−89.5409739087494x_{85} = -89.5409739087494
x86=43.993656070588x_{86} = 43.993656070588
x87=−29.8618536848212x_{87} = -29.8618536848212
x88=−23.5831053765957x_{88} = -23.5831053765957
x89=−17.3075449731851x_{89} = -17.3075449731851
x90=−97.3945054349341x_{90} = -97.3945054349341
x91=34.5719686876018x_{91} = 34.5719686876018
x92=12.6057680793701x_{92} = 12.6057680793701
x93=−81.687528885288x_{93} = -81.687528885288
x94=−87.9702772429881x_{94} = -87.9702772429881
x95=100.535937727896x_{95} = 100.535937727896
x96=31.431816577959x_{96} = 31.431816577959
x97=−3.28103371724202x_{97} = -3.28103371724202
x98=−45.5640613174892x_{98} = -45.5640613174892
x99=−67.5516420403464x_{99} = -67.5516420403464
x100=−83.2582097956514x_{100} = -83.2582097956514
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=0x_{1} = 0

lim⁡x→0−(4(tan⁡2(2x)+1)tan⁡(2x)−4(tan⁡2(2x)+1)x+3tan⁡(2x)x2x2)=−∞\lim_{x \to 0^-}\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} + \frac{3 \tan{\left(2 x \right)}}{x^{2}}}{x^{2}}\right) = -\infty
lim⁡x→0+(4(tan⁡2(2x)+1)tan⁡(2x)−4(tan⁡2(2x)+1)x+3tan⁡(2x)x2x2)=∞\lim_{x \to 0^+}\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} + \frac{3 \tan{\left(2 x \right)}}{x^{2}}}{x^{2}}\right) = \infty
- los límites no son iguales, signo
x1=0x_{1} = 0
- es el punto de flexión

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[100.535937727896,∞)\left[100.535937727896, \infty\right)
Convexa en los intervalos
(−∞,−100.535937727896]\left(-\infty, -100.535937727896\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
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)2x2)y = \lim_{x \to -\infty}\left(\frac{\tan{\left(2 x \right)}}{2 x^{2}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(tan⁡(2x)2x2)y = \lim_{x \to \infty}\left(\frac{\tan{\left(2 x \right)}}{2 x^{2}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(2*x)/((2*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→−∞(12x2tan⁡(2x)x)y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{2 x^{2}} \tan{\left(2 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(12x2tan⁡(2x)x)y = x \lim_{x \to \infty}\left(\frac{\frac{1}{2 x^{2}} \tan{\left(2 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:
tan⁡(2x)2x2=−12x2tan⁡(2x)\frac{\tan{\left(2 x \right)}}{2 x^{2}} = - \frac{1}{2 x^{2}} \tan{\left(2 x \right)}
- No
tan⁡(2x)2x2=12x2tan⁡(2x)\frac{\tan{\left(2 x \right)}}{2 x^{2}} = \frac{1}{2 x^{2}} \tan{\left(2 x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = tan(2*x)/((2*x^2))
    © Sr Examen – Калькулятор