Sr Examen

Otras calculadoras

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

Gráfico de la función y = x*cot(5*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*cot(5*x)
f(x)=xcot⁡(5x)f{\left(x \right)} = x \cot{\left(5 x \right)} 
f = x*cot(5*x)
Gráfico de la función
02468-8-6-4-2-1010-10001000
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:
xcot⁡(5x)=0x \cot{\left(5 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−9π10x_{1} = - \frac{9 \pi}{10}
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π10x_{3} = \frac{\pi}{10}
x4=π2x_{4} = \frac{\pi}{2}
x5=−ilog⁡(−105+58+25+58+i4+5i4)x_{5} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}
x6=−ilog⁡(−25+58+105+58−5i4−i4)x_{6} = - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}
x7=−ilog⁡(−105−516+25−516+25+516+105+516+i4+5i4)x_{7} = - i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}
x8=−ilog⁡(−105+516−25+516−25−516+105−516−5i4−i4)x_{8} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}
Solución numérica
x1=−9.73893722612836x_{1} = -9.73893722612836
x2=61.8893752757189x_{2} = 61.8893752757189
x3=−87.6504350351552x_{3} = -87.6504350351552
x4=46.18141200777x_{4} = 46.18141200777
x5=86.3937979737193x_{5} = 86.3937979737193
x6=56.2345084992573x_{6} = 56.2345084992573
x7=26.0752190247953x_{7} = 26.0752190247953
x8=42.4115008234622x_{8} = 42.4115008234622
x9=93.9336203423348x_{9} = 93.9336203423348
x10=54.3495529071034x_{10} = 54.3495529071034
x11=−1.5707963267949x_{11} = -1.5707963267949
x12=66.2876049907446x_{12} = 66.2876049907446
x13=−70.0575161750524x_{13} = -70.0575161750524
x14=92.0486647501809x_{14} = 92.0486647501809
x15=−5.96902604182061x_{15} = -5.96902604182061
x16=−41.7831822927443x_{16} = -41.7831822927443
x17=−55.6061899685393x_{17} = -55.6061899685393
x18=−60.0044196835651x_{18} = -60.0044196835651
x19=−51.8362787842316x_{19} = -51.8362787842316
x20=88.2787535658732x_{20} = 88.2787535658732
x21=10.3672557568463x_{21} = 10.3672557568463
x22=−99.5884871187965x_{22} = -99.5884871187965
x23=−49.9513231920777x_{23} = -49.9513231920777
x24=7.85398163397448x_{24} = 7.85398163397448
x25=−48.0663675999238x_{25} = -48.0663675999238
x26=17.9070781254618x_{26} = 17.9070781254618
x27=60.0044196835651x_{27} = 60.0044196835651
x28=−67.5442420521806x_{28} = -67.5442420521806
x29=38.0132711084365x_{29} = 38.0132711084365
x30=−4.08407044966673x_{30} = -4.08407044966673
x31=4.08407044966673x_{31} = 4.08407044966673
x32=96.4468944652067x_{32} = 96.4468944652067
x33=−77.5973385436679x_{33} = -77.5973385436679
x34=39.8982267005904x_{34} = 39.8982267005904
x35=−95.8185759344887x_{35} = -95.8185759344887
x36=−17.9070781254618x_{36} = -17.9070781254618
x37=−93.9336203423348x_{37} = -93.9336203423348
x38=22.3053078404875x_{38} = 22.3053078404875
x39=29.845130209103x_{39} = 29.845130209103
x40=98.3318500573605x_{40} = 98.3318500573605
x41=83.8805238508475x_{41} = 83.8805238508475
x42=−11.6238928182822x_{42} = -11.6238928182822
x43=80.1106126665397x_{43} = 80.1106126665397
x44=16.0221225333079x_{44} = 16.0221225333079
x45=−31.7300858012569x_{45} = -31.7300858012569
x46=12.2522113490002x_{46} = 12.2522113490002
x47=81.9955682586936x_{47} = 81.9955682586936
x48=−80.1106126665397x_{48} = -80.1106126665397
x49=−29.845130209103x_{49} = -29.845130209103
x50=70.0575161750524x_{50} = 70.0575161750524
x51=−61.8893752757189x_{51} = -61.8893752757189
x52=−53.7212343763855x_{52} = -53.7212343763855
x53=−81.9955682586936x_{53} = -81.9955682586936
x54=74.4557458900781x_{54} = 74.4557458900781
x55=44.2964564156161x_{55} = 44.2964564156161
x56=−39.8982267005904x_{56} = -39.8982267005904
x57=48.0663675999238x_{57} = 48.0663675999238
x58=2.19911485751286x_{58} = 2.19911485751286
x59=−85.7654794430014x_{59} = -85.7654794430014
x60=49.9513231920777x_{60} = 49.9513231920777
x61=−43.6681378848981x_{61} = -43.6681378848981
x62=20.4203522483337x_{62} = 20.4203522483337
x63=−71.9424717672063x_{63} = -71.9424717672063
x64=14.1371669411541x_{64} = 14.1371669411541
x65=100.216805649514x_{65} = 100.216805649514
x66=52.4645973149496x_{66} = 52.4645973149496
x67=−23.5619449019235x_{67} = -23.5619449019235
x68=−16.0221225333079x_{68} = -16.0221225333079
x69=−36.1283155162826x_{69} = -36.1283155162826
x70=90.1637091580271x_{70} = 90.1637091580271
x71=71.9424717672063x_{71} = 71.9424717672063
x72=−21.6769893097696x_{72} = -21.6769893097696
x73=78.2256570743859x_{73} = 78.2256570743859
x74=36.1283155162826x_{74} = 36.1283155162826
x75=−26.0752190247953x_{75} = -26.0752190247953
x76=−14.1371669411541x_{76} = -14.1371669411541
x77=76.340701482232x_{77} = 76.340701482232
x78=27.9601746169492x_{78} = 27.9601746169492
x79=24.1902634326414x_{79} = 24.1902634326414
x80=−89.5353906273091x_{80} = -89.5353906273091
x81=−19.7920337176157x_{81} = -19.7920337176157
x82=68.1725605828985x_{82} = 68.1725605828985
x83=−75.712382951514x_{83} = -75.712382951514
x84=−63.7743308678728x_{84} = -63.7743308678728
x85=−83.8805238508475x_{85} = -83.8805238508475
x86=−7.85398163397448x_{86} = -7.85398163397448
x87=64.4026493985908x_{87} = 64.4026493985908
x88=5.96902604182061x_{88} = 5.96902604182061
x89=−38.0132711084365x_{89} = -38.0132711084365
x90=−33.6150413934108x_{90} = -33.6150413934108
x91=−73.8274273593601x_{91} = -73.8274273593601
x92=−97.7035315266426x_{92} = -97.7035315266426
x93=32.3584043319749x_{93} = 32.3584043319749
x94=34.2433599241287x_{94} = 34.2433599241287
x95=−92.0486647501809x_{95} = -92.0486647501809
x96=−27.9601746169492x_{96} = -27.9601746169492
x97=−45.553093477052x_{97} = -45.553093477052
x98=−65.6592864600267x_{98} = -65.6592864600267
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 x*cot(5*x).
0cot⁡(0⋅5)0 \cot{\left(0 \cdot 5 \right)}
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
x(−5cot⁡2(5x)−5)+cot⁡(5x)=0x \left(- 5 \cot^{2}{\left(5 x \right)} - 5\right) + \cot{\left(5 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=5.57555085659956⋅10−19x_{1} = 5.57555085659956 \cdot 10^{-19}
x2=6.81265348238007⋅10−16x_{2} = 6.81265348238007 \cdot 10^{-16}
x3=−9.78262711255965⋅10−19x_{3} = -9.78262711255965 \cdot 10^{-19}
x4=−1.60553063072028⋅10−15x_{4} = -1.60553063072028 \cdot 10^{-15}
x5=−1.51658149098101⋅10−15x_{5} = -1.51658149098101 \cdot 10^{-15}
x6=−2.81142607877329⋅10−17x_{6} = -2.81142607877329 \cdot 10^{-17}
x7=−6.1123102028362⋅10−15x_{7} = -6.1123102028362 \cdot 10^{-15}
x8=4.2740423111762⋅10−15x_{8} = 4.2740423111762 \cdot 10^{-15}
x9=3.75244751272614⋅10−17x_{9} = 3.75244751272614 \cdot 10^{-17}
x10=5.84862855157776⋅10−19x_{10} = 5.84862855157776 \cdot 10^{-19}
x11=−1.79068425846629⋅10−15x_{11} = -1.79068425846629 \cdot 10^{-15}
x12=3.49031941668771⋅10−18x_{12} = 3.49031941668771 \cdot 10^{-18}
x13=1.2829291187686⋅10−15x_{13} = 1.2829291187686 \cdot 10^{-15}
x14=5.22852238320599⋅10−15x_{14} = 5.22852238320599 \cdot 10^{-15}
x15=2.42292982440693⋅10−16x_{15} = 2.42292982440693 \cdot 10^{-16}
x16=−8.31907369465597⋅10−16x_{16} = -8.31907369465597 \cdot 10^{-16}
x17=7.42720551692958⋅10−16x_{17} = 7.42720551692958 \cdot 10^{-16}
x18=6.26472183562438⋅10−19x_{18} = 6.26472183562438 \cdot 10^{-19}
x19=3.30182062527289⋅10−19x_{19} = 3.30182062527289 \cdot 10^{-19}
x20=−2.2911763306459⋅10−15x_{20} = -2.2911763306459 \cdot 10^{-15}
x21=6.89170953948765⋅10−17x_{21} = 6.89170953948765 \cdot 10^{-17}
x22=−1.99915042902958⋅10−16x_{22} = -1.99915042902958 \cdot 10^{-16}
x23=8.77733359713994⋅10−15x_{23} = 8.77733359713994 \cdot 10^{-15}
x24=5.41455832493694⋅10−18x_{24} = 5.41455832493694 \cdot 10^{-18}
x25=5.33376637221872⋅10−19x_{25} = 5.33376637221872 \cdot 10^{-19}
x26=4.55224153892282⋅10−15x_{26} = 4.55224153892282 \cdot 10^{-15}
x27=−1.12357796360712⋅10−18x_{27} = -1.12357796360712 \cdot 10^{-18}
x28=−8.80578974620273⋅10−17x_{28} = -8.80578974620273 \cdot 10^{-17}
x29=1.37238535528263⋅10−19x_{29} = 1.37238535528263 \cdot 10^{-19}
x30=−1.68184180030901⋅10−17x_{30} = -1.68184180030901 \cdot 10^{-17}
x31=−2.45010207903684⋅10−16x_{31} = -2.45010207903684 \cdot 10^{-16}
x32=9.13646408585193⋅10−17x_{32} = 9.13646408585193 \cdot 10^{-17}
x33=3.99221583653337⋅10−16x_{33} = 3.99221583653337 \cdot 10^{-16}
x34=−3.70835923109034⋅10−19x_{34} = -3.70835923109034 \cdot 10^{-19}
x35=4.54689261809182⋅10−16x_{35} = 4.54689261809182 \cdot 10^{-16}
x36=−2.04028471051634⋅10−16x_{36} = -2.04028471051634 \cdot 10^{-16}
x37=2.87946731399489⋅10−15x_{37} = 2.87946731399489 \cdot 10^{-15}
x38=−9.2175444749284⋅10−17x_{38} = -9.2175444749284 \cdot 10^{-17}
x39=−1.22855688279054⋅10−17x_{39} = -1.22855688279054 \cdot 10^{-17}
x40=−5.11451293663147⋅10−17x_{40} = -5.11451293663147 \cdot 10^{-17}
Signos de extremos en los puntos:
(5.575550856599561e-19, 0.2)

(6.812653482380068e-16, 0.2)

(-9.782627112559651e-19, 0.2)

(-1.6055306307202809e-15, 0.2)

(-1.51658149098101e-15, 0.2)

(-2.811426078773294e-17, 0.2)

(-6.112310202836199e-15, 0.2)

(4.274042311176198e-15, 0.2)

(3.7524475127261426e-17, 0.2)

(5.848628551577758e-19, 0.2)

(-1.7906842584662924e-15, 0.2)

(3.490319416687708e-18, 0.2)

(1.2829291187685987e-15, 0.2)

(5.228522383205988e-15, 0.2)

(2.422929824406927e-16, 0.2)

(-8.3190736946559705e-16, 0.2)

(7.427205516929585e-16, 0.2)

(6.264721835624376e-19, 0.2)

(3.3018206252728925e-19, 0.2)

(-2.291176330645898e-15, 0.2)

(6.891709539487645e-17, 0.2)

(-1.999150429029578e-16, 0.2)

(8.77733359713994e-15, 0.2)

(5.414558324936945e-18, 0.2)

(5.333766372218723e-19, 0.2)

(4.552241538922819e-15, 0.2)

(-1.1235779636071244e-18, 0.2)

(-8.805789746202735e-17, 0.2)

(1.3723853552826345e-19, 0.2)

(-1.6818418003090067e-17, 0.2)

(-2.450102079036836e-16, 0.2)

(9.136464085851934e-17, 0.2)

(3.992215836533367e-16, 0.2)

(-3.7083592310903383e-19, 0.2)

(4.546892618091817e-16, 0.2)

(-2.0402847105163394e-16, 0.2)

(2.879467313994889e-15, 0.2)

(-9.217544474928395e-17, 0.2)

(-1.2285568827905359e-17, 0.2)

(-5.1145129366314665e-17, 0.2)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
La función no tiene puntos mínimos
Puntos máximos de la función:
x40=5.57555085659956⋅10−19x_{40} = 5.57555085659956 \cdot 10^{-19}
x40=6.81265348238007⋅10−16x_{40} = 6.81265348238007 \cdot 10^{-16}
x40=−9.78262711255965⋅10−19x_{40} = -9.78262711255965 \cdot 10^{-19}
x40=−1.60553063072028⋅10−15x_{40} = -1.60553063072028 \cdot 10^{-15}
x40=−1.51658149098101⋅10−15x_{40} = -1.51658149098101 \cdot 10^{-15}
x40=−2.81142607877329⋅10−17x_{40} = -2.81142607877329 \cdot 10^{-17}
x40=−6.1123102028362⋅10−15x_{40} = -6.1123102028362 \cdot 10^{-15}
x40=4.2740423111762⋅10−15x_{40} = 4.2740423111762 \cdot 10^{-15}
x40=3.75244751272614⋅10−17x_{40} = 3.75244751272614 \cdot 10^{-17}
x40=5.84862855157776⋅10−19x_{40} = 5.84862855157776 \cdot 10^{-19}
x40=−1.79068425846629⋅10−15x_{40} = -1.79068425846629 \cdot 10^{-15}
x40=3.49031941668771⋅10−18x_{40} = 3.49031941668771 \cdot 10^{-18}
x40=1.2829291187686⋅10−15x_{40} = 1.2829291187686 \cdot 10^{-15}
x40=5.22852238320599⋅10−15x_{40} = 5.22852238320599 \cdot 10^{-15}
x40=2.42292982440693⋅10−16x_{40} = 2.42292982440693 \cdot 10^{-16}
x40=−8.31907369465597⋅10−16x_{40} = -8.31907369465597 \cdot 10^{-16}
x40=7.42720551692958⋅10−16x_{40} = 7.42720551692958 \cdot 10^{-16}
x40=6.26472183562438⋅10−19x_{40} = 6.26472183562438 \cdot 10^{-19}
x40=3.30182062527289⋅10−19x_{40} = 3.30182062527289 \cdot 10^{-19}
x40=−2.2911763306459⋅10−15x_{40} = -2.2911763306459 \cdot 10^{-15}
x40=6.89170953948765⋅10−17x_{40} = 6.89170953948765 \cdot 10^{-17}
x40=−1.99915042902958⋅10−16x_{40} = -1.99915042902958 \cdot 10^{-16}
x40=8.77733359713994⋅10−15x_{40} = 8.77733359713994 \cdot 10^{-15}
x40=5.41455832493694⋅10−18x_{40} = 5.41455832493694 \cdot 10^{-18}
x40=5.33376637221872⋅10−19x_{40} = 5.33376637221872 \cdot 10^{-19}
x40=4.55224153892282⋅10−15x_{40} = 4.55224153892282 \cdot 10^{-15}
x40=−1.12357796360712⋅10−18x_{40} = -1.12357796360712 \cdot 10^{-18}
x40=−8.80578974620273⋅10−17x_{40} = -8.80578974620273 \cdot 10^{-17}
x40=1.37238535528263⋅10−19x_{40} = 1.37238535528263 \cdot 10^{-19}
x40=−1.68184180030901⋅10−17x_{40} = -1.68184180030901 \cdot 10^{-17}
x40=−2.45010207903684⋅10−16x_{40} = -2.45010207903684 \cdot 10^{-16}
x40=9.13646408585193⋅10−17x_{40} = 9.13646408585193 \cdot 10^{-17}
x40=3.99221583653337⋅10−16x_{40} = 3.99221583653337 \cdot 10^{-16}
x40=−3.70835923109034⋅10−19x_{40} = -3.70835923109034 \cdot 10^{-19}
x40=4.54689261809182⋅10−16x_{40} = 4.54689261809182 \cdot 10^{-16}
x40=−2.04028471051634⋅10−16x_{40} = -2.04028471051634 \cdot 10^{-16}
x40=2.87946731399489⋅10−15x_{40} = 2.87946731399489 \cdot 10^{-15}
x40=−9.2175444749284⋅10−17x_{40} = -9.2175444749284 \cdot 10^{-17}
x40=−1.22855688279054⋅10−17x_{40} = -1.22855688279054 \cdot 10^{-17}
x40=−5.11451293663147⋅10−17x_{40} = -5.11451293663147 \cdot 10^{-17}
Decrece en los intervalos
(−∞,−6.1123102028362⋅10−15]\left(-\infty, -6.1123102028362 \cdot 10^{-15}\right]
Crece en los intervalos
[8.77733359713994⋅10−15,∞)\left[8.77733359713994 \cdot 10^{-15}, \infty\right)
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
10(5x(cot⁡2(5x)+1)cot⁡(5x)−cot⁡2(5x)−1)=010 \left(5 x \left(\cot^{2}{\left(5 x \right)} + 1\right) \cot{\left(5 x \right)} - \cot^{2}{\left(5 x \right)} - 1\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=64.4020283021367x_{1} = 64.4020283021367
x2=−67.5436498442796x_{2} = -67.5436498442796
x3=74.4552086556184x_{3} = 74.4552086556184
x4=−83.8800469802968x_{4} = -83.8800469802968
x5=−70.0569452125131x_{5} = -70.0569452125131
x6=−1.54505036738754x_{6} = -1.54505036738754
x7=−16.019625725789x_{7} = -16.019625725789
x8=−73.8268855526477x_{8} = -73.8268855526477
x9=14.1343371423239x_{9} = 14.1343371423239
x10=81.9950804255155x_{10} = 81.9950804255155
x11=44.2955533965743x_{11} = 44.2955533965743
x12=−38.0122188249304x_{12} = -38.0122188249304
x13=−87.6499786753114x_{13} = -87.6499786753114
x14=−11.6204509508991x_{14} = -11.6204509508991
x15=−49.9505224039313x_{15} = -49.9505224039313
x16=68.1719738331978x_{16} = 68.1719738331978
x17=−23.5602471676449x_{17} = -23.5602471676449
x18=10.3633964974559x_{18} = 10.3633964974559
x19=86.393334975867x_{19} = 86.393334975867
x20=93.9331945084242x_{20} = 93.9331945084242
x21=61.8887289567295x_{21} = 61.8887289567295
x22=100.216406513801x_{22} = 100.216406513801
x23=−17.9048441860834x_{23} = -17.9048441860834
x24=38.0122188249304x_{24} = 38.0122188249304
x25=−63.773703652162x_{25} = -63.773703652162
x26=−90.1632655190998x_{26} = -90.1632655190998
x27=16.019625725789x_{27} = 16.019625725789
x28=71.9419157645404x_{28} = 71.9419157645404
x29=−39.8972241329727x_{29} = -39.8972241329727
x30=54.3488169238437x_{30} = 54.3488169238437
x31=−51.8355071162431x_{31} = -51.8355071162431
x32=−26.0736849410777x_{32} = -26.0736849410777
x33=4.07426059185751x_{33} = 4.07426059185751
x34=36.1272083288406x_{34} = 36.1272083288406
x35=−93.9331945084242x_{35} = -93.9331945084242
x36=−41.7822249551553x_{36} = -41.7822249551553
x37=49.9505224039313x_{37} = 49.9505224039313
x38=20.4183932929815x_{38} = 20.4183932929815
x39=−97.703122123716x_{39} = -97.703122123716
x40=−55.6054706179599x_{40} = -55.6054706179599
x41=−7.84888647223284x_{41} = -7.84888647223284
x42=22.3035144492262x_{42} = 22.3035144492262
x43=−33.6138514218278x_{43} = -33.6138514218278
x44=−43.6672218724157x_{44} = -43.6672218724157
x45=−92.0482301960676x_{45} = -92.0482301960676
x46=−80.1101133548396x_{46} = -80.1101133548396
x47=90.1632655190998x_{47} = 90.1632655190998
x48=−21.6751439303349x_{48} = -21.6751439303349
x49=−53.7204897849762x_{49} = -53.7204897849762
x50=5.96231975817859x_{50} = 5.96231975817859
x51=−58.118775848386x_{51} = -58.118775848386
x52=92.0482301960676x_{52} = 92.0482301960676
x53=−45.5522153695297x_{53} = -45.5522153695297
x54=12.2489460520749x_{54} = 12.2489460520749
x55=26.0736849410777x_{55} = 26.0736849410777
x56=46.1805458475896x_{56} = 46.1805458475896
x57=83.8800469802968x_{57} = 83.8800469802968
x58=−48.0655354076095x_{58} = -48.0655354076095
x59=17.9048441860834x_{59} = 17.9048441860834
x60=−95.8181584776878x_{60} = -95.8181584776878
x61=58.118775848386x_{61} = 58.118775848386
x62=51.8355071162431x_{62} = 51.8355071162431
x63=88.2783004541645x_{63} = 88.2783004541645
x64=−81.9950804255155x_{64} = -81.9950804255155
x65=−77.5968230597879x_{65} = -77.5968230597879
x66=60.0037530610651x_{66} = 60.0037530610651
x67=−9.73482884639088x_{67} = -9.73482884639088
x68=70.0569452125131x_{68} = 70.0569452125131
x69=−14.1343371423239x_{69} = -14.1343371423239
x70=−27.9587439619171x_{70} = -27.9587439619171
x71=56.2337971862508x_{71} = 56.2337971862508
x72=39.8972241329727x_{72} = 39.8972241329727
x73=42.410557669076x_{73} = 42.410557669076
x74=−60.0037530610651x_{74} = -60.0037530610651
x75=−99.5880854648633x_{75} = -99.5880854648633
x76=34.2421917878891x_{76} = 34.2421917878891
x77=96.4464797280096x_{77} = 96.4464797280096
x78=76.3401775129436x_{78} = 76.3401775129436
x79=78.2251457309749x_{79} = 78.2251457309749
x80=−31.7288251346527x_{80} = -31.7288251346527
x81=−75.7118546338925x_{81} = -75.7118546338925
x82=2.18082433188578x_{82} = 2.18082433188578
x83=−36.1272083288406x_{83} = -36.1272083288406
x84=80.1101133548396x_{84} = 80.1101133548396
x85=7.84888647223284x_{85} = 7.84888647223284
x86=24.1886097994303x_{86} = 24.1886097994303
x87=−71.9419157645404x_{87} = -71.9419157645404
x88=32.3571681455931x_{88} = 32.3571681455931
x89=−29.843789916824x_{89} = -29.843789916824
x90=27.9587439619171x_{90} = 27.9587439619171
x91=48.0655354076095x_{91} = 48.0655354076095
x92=−85.7650130531989x_{92} = -85.7650130531989
x93=29.843789916824x_{93} = 29.843789916824
x94=66.2870015560186x_{94} = 66.2870015560186
x95=−65.6586772507346x_{95} = -65.6586772507346
x96=−4.07426059185751x_{96} = -4.07426059185751
x97=−19.7900125648664x_{97} = -19.7900125648664
x98=98.3314432704416x_{98} = 98.3314432704416
x99=−61.8887289567295x_{99} = -61.8887289567295
x100=−5.96231975817859x_{100} = -5.96231975817859

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
[−1.54505036738754,2.18082433188578]\left[-1.54505036738754, 2.18082433188578\right]
Convexa en los intervalos
(−∞,−99.5880854648633]\left(-\infty, -99.5880854648633\right]
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→−∞(xcot⁡(5x))y = \lim_{x \to -\infty}\left(x \cot{\left(5 x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(xcot⁡(5x))y = \lim_{x \to \infty}\left(x \cot{\left(5 x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*cot(5*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞cot⁡(5x)=−cot⁡(∞)\lim_{x \to -\infty} \cot{\left(5 x \right)} = - \cot{\left(\infty \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=−xcot⁡(∞)y = - x \cot{\left(\infty \right)}
lim⁡x→∞cot⁡(5x)=cot⁡(∞)\lim_{x \to \infty} \cot{\left(5 x \right)} = \cot{\left(\infty \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xcot⁡(∞)y = x \cot{\left(\infty \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:
xcot⁡(5x)=xcot⁡(5x)x \cot{\left(5 x \right)} = x \cot{\left(5 x \right)}
- Sí
xcot⁡(5x)=−xcot⁡(5x)x \cot{\left(5 x \right)} = - x \cot{\left(5 x \right)}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор