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Trazado el gráfico de la función/ sin(1000*x)*sqrt(3)/3*(10+sin(5-|x|)*|x|)

Gráfico de la función y = sin(1000*x)*sqrt(3)/3*(10+sin(5-|x|)*|x|)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                     ___                        
       sin(1000*x)*\/ 3                         
f(x) = -----------------*(10 + sin(5 - |x|)*|x|)
               3
f(x)=3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10)f{\left(x \right)} = \frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) 
f = ((sqrt(3)*sin(1000*x))/3)*(sin(5 - |x|)*|x| + 10)
Gráfico de la función
-4.0-3.0-2.0-1.04.00.01.02.03.0-2020
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:
3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10)=0\frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−99.10154025749x_{1} = -99.10154025749
x2=40.2469434851388x_{2} = 40.2469434851388
x3=−67.9777818383759x_{3} = -67.9777818383759
x4=−51.9430929344536x_{4} = -51.9430929344536
x5=5.74597296341573x_{5} = 5.74597296341573
x6=89.7898596322499x_{6} = 89.7898596322499
x7=−64.5345962900415x_{7} = -64.5345962900415
x8=−8.61110546348962x_{8} = -8.61110546348962
x9=99.3486060187879x_{9} = 99.3486060187879
x10=86.8336209452219x_{10} = 86.8336209452219
x11=−17.7499984927823x_{11} = -17.7499984927823
x12=61.7228708650787x_{12} = 61.7228708650787
x13=23.4080068618976x_{13} = 23.4080068618976
x14=−33.7249971362864x_{14} = -33.7249971362864
x15=58.2294198342868x_{15} = 58.2294198342868
x16=−61.7114299857102x_{16} = -61.7114299857102
x17=−24.2279625444845x_{17} = -24.2279625444845
x18=−58.219995056326x_{18} = -58.219995056326
x19=−26.5935818126376x_{19} = -26.5935818126376
x20=45.6159253301238x_{20} = 45.6159253301238
x21=−67.1546845631354x_{21} = -67.1546845631354
x22=18.1498936480029x_{22} = 18.1498936480029
x23=−83.4187097307698x_{23} = -83.4187097307698
x24=−81.5463205092303x_{24} = -81.5463205092303
x25=−67.979492029775x_{25} = -67.979492029775
x26=82.253178856288x_{26} = 82.253178856288
x27=−89.7144614085637x_{27} = -89.7144614085637
x28=67.9809234310295x_{28} = 67.9809234310295
x29=36.684377415968x_{29} = 36.684377415968
x30=−80.5227336754012x_{30} = -80.5227336754012
x31=−30.5676965194287x_{31} = -30.5676965194287
x32=−7.69690200129499x_{32} = -7.69690200129499
x33=−58.2325614269404x_{33} = -58.2325614269404
x34=−49.1870300318029x_{34} = -49.1870300318029
x35=−55.4522519285134x_{35} = -55.4522519285134
x36=0x_{36} = 0
x37=30.2723868099912x_{37} = 30.2723868099912
x38=−53.8154821559932x_{38} = -53.8154821559932
x39=−23.772431609714x_{39} = -23.772431609714
x40=20.1897831111952x_{40} = 20.1897831111952
x41=−15.9844234214649x_{41} = -15.9844234214649
x42=−13.5842466341223x_{42} = -13.5842466341223
x43=74.2641087382091x_{43} = 74.2641087382091
x44=−97.3799474833228x_{44} = -97.3799474833228
x45=61.7114299857102x_{45} = 61.7114299857102
x46=36.7063685645431x_{46} = 36.7063685645431
x47=−71.0188435270509x_{47} = -71.0188435270509
x48=−26.6030065905984x_{48} = -26.6030065905984
x49=24.2499536930596x_{49} = 24.2499536930596
x50=9.62583989059913x_{50} = 9.62583989059913
x51=21.6707061244624x_{51} = 21.6707061244624
x52=−49.7219869283657x_{52} = -49.7219869283657
x53=12.2394291586115x_{53} = 12.2394291586115
x54=47.9438454864338x_{54} = 47.9438454864338
x55=−73.7677370989419x_{55} = -73.7677370989419
x56=74.2501287922262x_{56} = 74.2501287922262
x57=−55.4585351138206x_{57} = -55.4585351138206
x58=80.5190197115064x_{58} = 80.5190197115064
x59=−39.6594656589175x_{59} = -39.6594656589175
x60=−61.7134460871179x_{60} = -61.7134460871179
x61=−43.7466777012379x_{61} = -43.7466777012379
x62=−21.903183980828x_{62} = -21.903183980828
x63=−75.7437988780499x_{63} = -75.7437988780499
x64=50.8403939130436x_{64} = 50.8403939130436
x65=−95.9976467157433x_{65} = -95.9976467157433
x66=−45.7227394803459x_{66} = -45.7227394803459
x67=−6.0004419683565x_{67} = -6.0004419683565
x68=−94.2666291636153x_{68} = -94.2666291636153
x69=−12.4124325743333x_{69} = -12.4124325743333
x70=31.89030702659x_{70} = 31.89030702659
x71=4.88831816898572x_{71} = 4.88831816898572
x72=−36.0780500338252x_{72} = -36.0780500338252
x73=12.2396449783858x_{73} = 12.2396449783858
x74=32.6819883752946x_{74} = 32.6819883752946
x75=42.9392883892653x_{75} = 42.9392883892653
x76=61.7134460871179x_{76} = 61.7134460871179
x77=94.1629566060469x_{77} = 94.1629566060469
x78=−85.7780458136157x_{78} = -85.7780458136157
x79=70.831792937014x_{79} = 70.831792937014
x80=−20.1533168727785x_{80} = -20.1533168727785
x81=51.9305265638393x_{81} = 51.9305265638393
x82=98.2501686483672x_{82} = 98.2501686483672
x83=96.0018329812683x_{83} = 96.0018329812683
x84=45.5028279945946x_{84} = 45.5028279945946
x85=−13.5999545973902x_{85} = -13.5999545973902
x86=32.572032632419x_{86} = 32.572032632419
x87=−36.6906606012752x_{87} = -36.6906606012752
x88=78.0874269976279x_{88} = 78.0874269976279
x89=−74.609683930104x_{89} = -74.609683930104
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(1000*x)*sqrt(3))/3)*(10 + sin(5 - |x|)*|x|).
3sin⁡(0⋅1000)3(sin⁡(5−∣0∣)∣0∣+10)\frac{\sqrt{3} \sin{\left(0 \cdot 1000 \right)}}{3} \left(\sin{\left(5 - \left|{0}\right| \right)} \left|{0}\right| + 10\right)
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 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→−∞(3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10))y = \lim_{x \to -\infty}\left(\frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right)\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10))y = \lim_{x \to \infty}\left(\frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right)\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función ((sin(1000*x)*sqrt(3))/3)*(10 + sin(5 - |x|)*|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→−∞(3(sin⁡(5−∣x∣)∣x∣+10)sin⁡(1000x)3x)y = x \lim_{x \to -\infty}\left(\frac{\sqrt{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) \sin{\left(1000 x \right)}}{3 x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(3(sin⁡(5−∣x∣)∣x∣+10)sin⁡(1000x)3x)y = x \lim_{x \to \infty}\left(\frac{\sqrt{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) \sin{\left(1000 x \right)}}{3 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:
3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10)=−3(sin⁡(5−∣x∣)∣x∣+10)sin⁡(1000x)3\frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) = - \frac{\sqrt{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) \sin{\left(1000 x \right)}}{3}
- No
3sin⁡(1000x)3(sin⁡(5−∣x∣)∣x∣+10)=3(sin⁡(5−∣x∣)∣x∣+10)sin⁡(1000x)3\frac{\sqrt{3} \sin{\left(1000 x \right)}}{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) = \frac{\sqrt{3} \left(\sin{\left(5 - \left|{x}\right| \right)} \left|{x}\right| + 10\right) \sin{\left(1000 x \right)}}{3}
- No
es decir, función
no es
par ni impar
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