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

Gráfico de la función y = (x)*cot(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*cot(x)
f(x)=xcot⁡(x)f{\left(x \right)} = x \cot{\left(x \right)} 
f = x*cot(x)
Gráfico de la función
02468-8-6-4-2-1010-50005000
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⁡(x)=0x \cot{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π2x_{1} = - \frac{\pi}{2}
x2=π2x_{2} = \frac{\pi}{2}
Solución numérica
x1=7.85398163397448x_{1} = 7.85398163397448
x2=−73.8274273593601x_{2} = -73.8274273593601
x3=−54.9778714378214x_{3} = -54.9778714378214
x4=73.8274273593601x_{4} = 73.8274273593601
x5=−26.7035375555132x_{5} = -26.7035375555132
x6=−1.5707963267949x_{6} = -1.5707963267949
x7=−95.8185759344887x_{7} = -95.8185759344887
x8=−39.2699081698724x_{8} = -39.2699081698724
x9=−4.71238898038469x_{9} = -4.71238898038469
x10=14.1371669411541x_{10} = 14.1371669411541
x11=10.9955742875643x_{11} = 10.9955742875643
x12=58.1194640914112x_{12} = 58.1194640914112
x13=70.6858347057703x_{13} = 70.6858347057703
x14=−36.1283155162826x_{14} = -36.1283155162826
x15=54.9778714378214x_{15} = 54.9778714378214
x16=23.5619449019235x_{16} = 23.5619449019235
x17=−92.6769832808989x_{17} = -92.6769832808989
x18=−86.3937979737193x_{18} = -86.3937979737193
x19=−10.9955742875643x_{19} = -10.9955742875643
x20=92.6769832808989x_{20} = 92.6769832808989
x21=39.2699081698724x_{21} = 39.2699081698724
x22=−32.9867228626928x_{22} = -32.9867228626928
x23=98.9601685880785x_{23} = 98.9601685880785
x24=36.1283155162826x_{24} = 36.1283155162826
x25=−7.85398163397448x_{25} = -7.85398163397448
x26=−58.1194640914112x_{26} = -58.1194640914112
x27=−67.5442420521806x_{27} = -67.5442420521806
x28=−61.261056745001x_{28} = -61.261056745001
x29=26.7035375555132x_{29} = 26.7035375555132
x30=86.3937979737193x_{30} = 86.3937979737193
x31=−48.6946861306418x_{31} = -48.6946861306418
x32=51.8362787842316x_{32} = 51.8362787842316
x33=−42.4115008234622x_{33} = -42.4115008234622
x34=−89.5353906273091x_{34} = -89.5353906273091
x35=−98.9601685880785x_{35} = -98.9601685880785
x36=−14.1371669411541x_{36} = -14.1371669411541
x37=80.1106126665397x_{37} = 80.1106126665397
x38=−64.4026493985908x_{38} = -64.4026493985908
x39=95.8185759344887x_{39} = 95.8185759344887
x40=1.5707963267949x_{40} = 1.5707963267949
x41=45.553093477052x_{41} = 45.553093477052
x42=−17.2787595947439x_{42} = -17.2787595947439
x43=4.71238898038469x_{43} = 4.71238898038469
x44=48.6946861306418x_{44} = 48.6946861306418
x45=76.9690200129499x_{45} = 76.9690200129499
x46=−45.553093477052x_{46} = -45.553093477052
x47=20.4203522483337x_{47} = 20.4203522483337
x48=17.2787595947439x_{48} = 17.2787595947439
x49=−83.2522053201295x_{49} = -83.2522053201295
x50=−20.4203522483337x_{50} = -20.4203522483337
x51=−80.1106126665397x_{51} = -80.1106126665397
x52=61.261056745001x_{52} = 61.261056745001
x53=32.9867228626928x_{53} = 32.9867228626928
x54=64.4026493985908x_{54} = 64.4026493985908
x55=−23.5619449019235x_{55} = -23.5619449019235
x56=29.845130209103x_{56} = 29.845130209103
x57=42.4115008234622x_{57} = 42.4115008234622
x58=89.5353906273091x_{58} = 89.5353906273091
x59=−51.8362787842316x_{59} = -51.8362787842316
x60=−70.6858347057703x_{60} = -70.6858347057703
x61=83.2522053201295x_{61} = 83.2522053201295
x62=67.5442420521806x_{62} = 67.5442420521806
x63=−29.845130209103x_{63} = -29.845130209103
x64=−76.9690200129499x_{64} = -76.9690200129499
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(x).
0cot⁡(0)0 \cot{\left(0 \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(−cot⁡2(x)−1)+cot⁡(x)=0x \left(- \cot^{2}{\left(x \right)} - 1\right) + \cot{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=4.14233733555801⋅10−16x_{1} = 4.14233733555801 \cdot 10^{-16}
x2=1.45362353365198⋅10−17x_{2} = 1.45362353365198 \cdot 10^{-17}
x3=−5.64340139631369⋅10−18x_{3} = -5.64340139631369 \cdot 10^{-18}
x4=3.24454072651749⋅10−18x_{4} = 3.24454072651749 \cdot 10^{-18}
x5=−1.0336014449672⋅10−15x_{5} = -1.0336014449672 \cdot 10^{-15}
x6=2.89656109220715⋅10−16x_{6} = 2.89656109220715 \cdot 10^{-16}
x7=−3.620858317633⋅10−15x_{7} = -3.620858317633 \cdot 10^{-15}
x8=1.61904873943669⋅10−15x_{8} = 1.61904873943669 \cdot 10^{-15}
x9=1.26980414917627⋅10−14x_{9} = 1.26980414917627 \cdot 10^{-14}
x10=−4.06279101811881⋅10−17x_{10} = -4.06279101811881 \cdot 10^{-17}
x11=−2.71634387267654⋅10−15x_{11} = -2.71634387267654 \cdot 10^{-15}
x12=−5.55874660801856⋅10−15x_{12} = -5.55874660801856 \cdot 10^{-15}
x13=1.44474290131774⋅10−18x_{13} = 1.44474290131774 \cdot 10^{-18}
x14=1.2403471803931⋅10−18x_{14} = 1.2403471803931 \cdot 10^{-18}
x15=1.25912856578362⋅10−18x_{15} = 1.25912856578362 \cdot 10^{-18}
x16=6.07020865447997⋅10−19x_{16} = 6.07020865447997 \cdot 10^{-19}
x17=3.11132936961652⋅10−13x_{17} = 3.11132936961652 \cdot 10^{-13}
x18=−1.01922295710768⋅10−15x_{18} = -1.01922295710768 \cdot 10^{-15}
x19=1.1749225530677⋅10−17x_{19} = 1.1749225530677 \cdot 10^{-17}
x20=−2.10428377845423⋅10−19x_{20} = -2.10428377845423 \cdot 10^{-19}
x21=−8.00122769767989⋅10−15x_{21} = -8.00122769767989 \cdot 10^{-15}
x22=4.5847372435963⋅10−15x_{22} = 4.5847372435963 \cdot 10^{-15}
x23=−5.745550974241⋅10−17x_{23} = -5.745550974241 \cdot 10^{-17}
x24=−3.51090745762135⋅10−15x_{24} = -3.51090745762135 \cdot 10^{-15}
x25=−6.40821132707816⋅10−15x_{25} = -6.40821132707816 \cdot 10^{-15}
x26=−1.98274474791319⋅10−16x_{26} = -1.98274474791319 \cdot 10^{-16}
x27=−4.40909774211023⋅10−17x_{27} = -4.40909774211023 \cdot 10^{-17}
x28=4.38463104684664⋅10−16x_{28} = 4.38463104684664 \cdot 10^{-16}
x29=−1.49427676404117⋅10−16x_{29} = -1.49427676404117 \cdot 10^{-16}
x30=−6.61342656563683⋅10−19x_{30} = -6.61342656563683 \cdot 10^{-19}
x31=−4.92334203842595⋅10−15x_{31} = -4.92334203842595 \cdot 10^{-15}
x32=−5.99685278638184⋅10−16x_{32} = -5.99685278638184 \cdot 10^{-16}
x33=4.94904520367816⋅10−19x_{33} = 4.94904520367816 \cdot 10^{-19}
x34=−2.04733750361427⋅10−15x_{34} = -2.04733750361427 \cdot 10^{-15}
x35=−1.79387879992692⋅10−17x_{35} = -1.79387879992692 \cdot 10^{-17}
x36=2.64478262616224⋅10−17x_{36} = 2.64478262616224 \cdot 10^{-17}
x37=−1.5594946391662⋅10−15x_{37} = -1.5594946391662 \cdot 10^{-15}
x38=1.65370221642112⋅10−15x_{38} = 1.65370221642112 \cdot 10^{-15}
x39=1.73191897241912⋅10−19x_{39} = 1.73191897241912 \cdot 10^{-19}
x40=−1.88300342913155⋅10−15x_{40} = -1.88300342913155 \cdot 10^{-15}
x41=2.72320120731057⋅10−14x_{41} = 2.72320120731057 \cdot 10^{-14}
x42=−9.87053303721349⋅10−18x_{42} = -9.87053303721349 \cdot 10^{-18}
x43=−9.70142387919427⋅10−15x_{43} = -9.70142387919427 \cdot 10^{-15}
x44=−7.17820192753118⋅10−17x_{44} = -7.17820192753118 \cdot 10^{-17}
x45=2.71254570988687⋅10−17x_{45} = 2.71254570988687 \cdot 10^{-17}
x46=−3.28203040887896⋅10−19x_{46} = -3.28203040887896 \cdot 10^{-19}
x47=1.15626527833042⋅10−14x_{47} = 1.15626527833042 \cdot 10^{-14}
x48=−1.59933915115257⋅10−17x_{48} = -1.59933915115257 \cdot 10^{-17}
x49=−2.2475411221051⋅10−18x_{49} = -2.2475411221051 \cdot 10^{-18}
x50=−6.82906419646335⋅10−18x_{50} = -6.82906419646335 \cdot 10^{-18}
x51=−6.15762676583726⋅10−19x_{51} = -6.15762676583726 \cdot 10^{-19}
x52=−1.10028462562426⋅10−15x_{52} = -1.10028462562426 \cdot 10^{-15}
x53=−4.18830978571137⋅10−16x_{53} = -4.18830978571137 \cdot 10^{-16}
x54=−1.1313309676076⋅10−16x_{54} = -1.1313309676076 \cdot 10^{-16}
x55=−5.8555151294134⋅10−19x_{55} = -5.8555151294134 \cdot 10^{-19}
x56=−6.42168942773399⋅10−16x_{56} = -6.42168942773399 \cdot 10^{-16}
x57=−1.87511913076322⋅10−14x_{57} = -1.87511913076322 \cdot 10^{-14}
x58=4.9014381205221⋅10−16x_{58} = 4.9014381205221 \cdot 10^{-16}
x59=1.06627540671766⋅10−14x_{59} = 1.06627540671766 \cdot 10^{-14}
x60=3.16309354089764⋅10−18x_{60} = 3.16309354089764 \cdot 10^{-18}
x61=−2.68607051572303⋅10−17x_{61} = -2.68607051572303 \cdot 10^{-17}
x62=−8.05253613839673⋅10−18x_{62} = -8.05253613839673 \cdot 10^{-18}
x63=1.74173497722007⋅10−14x_{63} = 1.74173497722007 \cdot 10^{-14}
x64=1.65999039586112⋅10−17x_{64} = 1.65999039586112 \cdot 10^{-17}
x65=−1.51633707509715⋅10−16x_{65} = -1.51633707509715 \cdot 10^{-16}
Signos de extremos en los puntos:
(4.142337335558013e-16, 1)

(1.4536235336519808e-17, 1)

(-5.643401396313692e-18, 1)

(3.244540726517495e-18, 1)

(-1.0336014449671976e-15, 1)

(2.896561092207152e-16, 1)

(-3.620858317633002e-15, 1)

(1.619048739436685e-15, 1)

(1.2698041491762749e-14, 1)

(-4.062791018118812e-17, 1)

(-2.7163438726765407e-15, 1)

(-5.558746608018558e-15, 1)

(1.4447429013177414e-18, 1)

(1.2403471803931023e-18, 1)

(1.2591285657836205e-18, 1)

(6.070208654479967e-19, 1)

(3.1113293696165157e-13, 1)

(-1.019222957107677e-15, 1)

(1.1749225530677002e-17, 1)

(-2.104283778454231e-19, 1)

(-8.001227697679886e-15, 1)

(4.584737243596305e-15, 1)

(-5.745550974240997e-17, 1)

(-3.5109074576213455e-15, 1)

(-6.408211327078158e-15, 1)

(-1.9827447479131868e-16, 1)

(-4.409097742110226e-17, 1)

(4.38463104684664e-16, 1)

(-1.4942767640411654e-16, 1)

(-6.613426565636826e-19, 1)

(-4.923342038425946e-15, 1)

(-5.996852786381843e-16, 1)

(4.949045203678157e-19, 1)

(-2.0473375036142655e-15, 1)

(-1.793878799926921e-17, 1)

(2.644782626162242e-17, 1)

(-1.5594946391661973e-15, 1)

(1.6537022164211227e-15, 1)

(1.731918972419121e-19, 1)

(-1.8830034291315523e-15, 1)

(2.7232012073105654e-14, 1)

(-9.870533037213493e-18, 1)

(-9.701423879194267e-15, 1)

(-7.178201927531184e-17, 1)

(2.7125457098868662e-17, 1)

(-3.282030408878956e-19, 1)

(1.1562652783304189e-14, 1)

(-1.5993391511525723e-17, 1)

(-2.2475411221050973e-18, 1)

(-6.8290641964633494e-18, 1)

(-6.157626765837259e-19, 1)

(-1.100284625624258e-15, 1)

(-4.188309785711367e-16, 1)

(-1.1313309676075998e-16, 1)

(-5.855515129413405e-19, 1)

(-6.421689427733992e-16, 1)

(-1.875119130763221e-14, 1)

(4.9014381205221e-16, 1)

(1.0662754067176585e-14, 1)

(3.16309354089764e-18, 1)

(-2.6860705157230273e-17, 1)

(-8.052536138396728e-18, 1)

(1.7417349772200653e-14, 1)

(1.659990395861115e-17, 1)

(-1.5163370750971476e-16, 1)


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:
x65=4.14233733555801⋅10−16x_{65} = 4.14233733555801 \cdot 10^{-16}
x65=1.45362353365198⋅10−17x_{65} = 1.45362353365198 \cdot 10^{-17}
x65=−5.64340139631369⋅10−18x_{65} = -5.64340139631369 \cdot 10^{-18}
x65=3.24454072651749⋅10−18x_{65} = 3.24454072651749 \cdot 10^{-18}
x65=−1.0336014449672⋅10−15x_{65} = -1.0336014449672 \cdot 10^{-15}
x65=2.89656109220715⋅10−16x_{65} = 2.89656109220715 \cdot 10^{-16}
x65=−3.620858317633⋅10−15x_{65} = -3.620858317633 \cdot 10^{-15}
x65=1.61904873943669⋅10−15x_{65} = 1.61904873943669 \cdot 10^{-15}
x65=1.26980414917627⋅10−14x_{65} = 1.26980414917627 \cdot 10^{-14}
x65=−4.06279101811881⋅10−17x_{65} = -4.06279101811881 \cdot 10^{-17}
x65=−2.71634387267654⋅10−15x_{65} = -2.71634387267654 \cdot 10^{-15}
x65=−5.55874660801856⋅10−15x_{65} = -5.55874660801856 \cdot 10^{-15}
x65=1.44474290131774⋅10−18x_{65} = 1.44474290131774 \cdot 10^{-18}
x65=1.2403471803931⋅10−18x_{65} = 1.2403471803931 \cdot 10^{-18}
x65=1.25912856578362⋅10−18x_{65} = 1.25912856578362 \cdot 10^{-18}
x65=6.07020865447997⋅10−19x_{65} = 6.07020865447997 \cdot 10^{-19}
x65=3.11132936961652⋅10−13x_{65} = 3.11132936961652 \cdot 10^{-13}
x65=−1.01922295710768⋅10−15x_{65} = -1.01922295710768 \cdot 10^{-15}
x65=1.1749225530677⋅10−17x_{65} = 1.1749225530677 \cdot 10^{-17}
x65=−2.10428377845423⋅10−19x_{65} = -2.10428377845423 \cdot 10^{-19}
x65=−8.00122769767989⋅10−15x_{65} = -8.00122769767989 \cdot 10^{-15}
x65=4.5847372435963⋅10−15x_{65} = 4.5847372435963 \cdot 10^{-15}
x65=−5.745550974241⋅10−17x_{65} = -5.745550974241 \cdot 10^{-17}
x65=−3.51090745762135⋅10−15x_{65} = -3.51090745762135 \cdot 10^{-15}
x65=−6.40821132707816⋅10−15x_{65} = -6.40821132707816 \cdot 10^{-15}
x65=−1.98274474791319⋅10−16x_{65} = -1.98274474791319 \cdot 10^{-16}
x65=−4.40909774211023⋅10−17x_{65} = -4.40909774211023 \cdot 10^{-17}
x65=4.38463104684664⋅10−16x_{65} = 4.38463104684664 \cdot 10^{-16}
x65=−1.49427676404117⋅10−16x_{65} = -1.49427676404117 \cdot 10^{-16}
x65=−6.61342656563683⋅10−19x_{65} = -6.61342656563683 \cdot 10^{-19}
x65=−4.92334203842595⋅10−15x_{65} = -4.92334203842595 \cdot 10^{-15}
x65=−5.99685278638184⋅10−16x_{65} = -5.99685278638184 \cdot 10^{-16}
x65=4.94904520367816⋅10−19x_{65} = 4.94904520367816 \cdot 10^{-19}
x65=−2.04733750361427⋅10−15x_{65} = -2.04733750361427 \cdot 10^{-15}
x65=−1.79387879992692⋅10−17x_{65} = -1.79387879992692 \cdot 10^{-17}
x65=2.64478262616224⋅10−17x_{65} = 2.64478262616224 \cdot 10^{-17}
x65=−1.5594946391662⋅10−15x_{65} = -1.5594946391662 \cdot 10^{-15}
x65=1.65370221642112⋅10−15x_{65} = 1.65370221642112 \cdot 10^{-15}
x65=1.73191897241912⋅10−19x_{65} = 1.73191897241912 \cdot 10^{-19}
x65=−1.88300342913155⋅10−15x_{65} = -1.88300342913155 \cdot 10^{-15}
x65=2.72320120731057⋅10−14x_{65} = 2.72320120731057 \cdot 10^{-14}
x65=−9.87053303721349⋅10−18x_{65} = -9.87053303721349 \cdot 10^{-18}
x65=−9.70142387919427⋅10−15x_{65} = -9.70142387919427 \cdot 10^{-15}
x65=−7.17820192753118⋅10−17x_{65} = -7.17820192753118 \cdot 10^{-17}
x65=2.71254570988687⋅10−17x_{65} = 2.71254570988687 \cdot 10^{-17}
x65=−3.28203040887896⋅10−19x_{65} = -3.28203040887896 \cdot 10^{-19}
x65=1.15626527833042⋅10−14x_{65} = 1.15626527833042 \cdot 10^{-14}
x65=−1.59933915115257⋅10−17x_{65} = -1.59933915115257 \cdot 10^{-17}
x65=−2.2475411221051⋅10−18x_{65} = -2.2475411221051 \cdot 10^{-18}
x65=−6.82906419646335⋅10−18x_{65} = -6.82906419646335 \cdot 10^{-18}
x65=−6.15762676583726⋅10−19x_{65} = -6.15762676583726 \cdot 10^{-19}
x65=−1.10028462562426⋅10−15x_{65} = -1.10028462562426 \cdot 10^{-15}
x65=−4.18830978571137⋅10−16x_{65} = -4.18830978571137 \cdot 10^{-16}
x65=−1.1313309676076⋅10−16x_{65} = -1.1313309676076 \cdot 10^{-16}
x65=−5.8555151294134⋅10−19x_{65} = -5.8555151294134 \cdot 10^{-19}
x65=−6.42168942773399⋅10−16x_{65} = -6.42168942773399 \cdot 10^{-16}
x65=−1.87511913076322⋅10−14x_{65} = -1.87511913076322 \cdot 10^{-14}
x65=4.9014381205221⋅10−16x_{65} = 4.9014381205221 \cdot 10^{-16}
x65=1.06627540671766⋅10−14x_{65} = 1.06627540671766 \cdot 10^{-14}
x65=3.16309354089764⋅10−18x_{65} = 3.16309354089764 \cdot 10^{-18}
x65=−2.68607051572303⋅10−17x_{65} = -2.68607051572303 \cdot 10^{-17}
x65=−8.05253613839673⋅10−18x_{65} = -8.05253613839673 \cdot 10^{-18}
x65=1.74173497722007⋅10−14x_{65} = 1.74173497722007 \cdot 10^{-14}
x65=1.65999039586112⋅10−17x_{65} = 1.65999039586112 \cdot 10^{-17}
x65=−1.51633707509715⋅10−16x_{65} = -1.51633707509715 \cdot 10^{-16}
Decrece en los intervalos
(−∞,−1.87511913076322⋅10−14]\left(-\infty, -1.87511913076322 \cdot 10^{-14}\right]
Crece en los intervalos
[3.11132936961652⋅10−13,∞)\left[3.11132936961652 \cdot 10^{-13}, \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
2(x(cot⁡2(x)+1)cot⁡(x)−cot⁡2(x)−1)=02 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \cot^{2}{\left(x \right)} - 1\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−58.1022547544956x_{1} = -58.1022547544956
x2=51.8169824872797x_{2} = 51.8169824872797
x3=73.8138806006806x_{3} = 73.8138806006806
x4=92.6661922776228x_{4} = 92.6661922776228
x5=−14.0661939128315x_{5} = -14.0661939128315
x6=70.6716857116195x_{6} = 70.6716857116195
x7=−67.5294347771441x_{7} = -67.5294347771441
x8=45.5311340139913x_{8} = 45.5311340139913
x9=39.2444323611642x_{9} = 39.2444323611642
x10=−54.9596782878889x_{10} = -54.9596782878889
x11=−32.9563890398225x_{11} = -32.9563890398225
x12=89.5242209304172x_{12} = 89.5242209304172
x13=−70.6716857116195x_{13} = -70.6716857116195
x14=14.0661939128315x_{14} = 14.0661939128315
x15=−61.2447302603744x_{15} = -61.2447302603744
x16=86.3822220347287x_{16} = 86.3822220347287
x17=−64.3871195905574x_{17} = -64.3871195905574
x18=26.6660542588127x_{18} = 26.6660542588127
x19=95.8081387868617x_{19} = 95.8081387868617
x20=−17.2207552719308x_{20} = -17.2207552719308
x21=−36.1006222443756x_{21} = -36.1006222443756
x22=−42.3879135681319x_{22} = -42.3879135681319
x23=−92.6661922776228x_{23} = -92.6661922776228
x24=−76.9560263103312x_{24} = -76.9560263103312
x25=80.0981286289451x_{25} = 80.0981286289451
x26=−86.3822220347287x_{26} = -86.3822220347287
x27=−29.811598790893x_{27} = -29.811598790893
x28=10.9041216594289x_{28} = 10.9041216594289
x29=−89.5242209304172x_{29} = -89.5242209304172
x30=−48.6741442319544x_{30} = -48.6741442319544
x31=54.9596782878889x_{31} = 54.9596782878889
x32=23.519452498689x_{32} = 23.519452498689
x33=−51.8169824872797x_{33} = -51.8169824872797
x34=42.3879135681319x_{34} = 42.3879135681319
x35=−83.2401924707234x_{35} = -83.2401924707234
x36=48.6741442319544x_{36} = 48.6741442319544
x37=−39.2444323611642x_{37} = -39.2444323611642
x38=−23.519452498689x_{38} = -23.519452498689
x39=−7.72525183693771x_{39} = -7.72525183693771
x40=67.5294347771441x_{40} = 67.5294347771441
x41=61.2447302603744x_{41} = 61.2447302603744
x42=4.49340945790906x_{42} = 4.49340945790906
x43=36.1006222443756x_{43} = 36.1006222443756
x44=32.9563890398225x_{44} = 32.9563890398225
x45=20.3713029592876x_{45} = 20.3713029592876
x46=83.2401924707234x_{46} = 83.2401924707234
x47=−98.9500628243319x_{47} = -98.9500628243319
x48=58.1022547544956x_{48} = 58.1022547544956
x49=−45.5311340139913x_{49} = -45.5311340139913
x50=−95.8081387868617x_{50} = -95.8081387868617
x51=−26.6660542588127x_{51} = -26.6660542588127
x52=−20.3713029592876x_{52} = -20.3713029592876
x53=98.9500628243319x_{53} = 98.9500628243319
x54=−4.49340945790906x_{54} = -4.49340945790906
x55=64.3871195905574x_{55} = 64.3871195905574
x56=7.72525183693771x_{56} = 7.72525183693771
x57=−80.0981286289451x_{57} = -80.0981286289451
x58=−10.9041216594289x_{58} = -10.9041216594289
x59=76.9560263103312x_{59} = 76.9560263103312
x60=29.811598790893x_{60} = 29.811598790893
x61=17.2207552719308x_{61} = 17.2207552719308
x62=−73.8138806006806x_{62} = -73.8138806006806

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
[−4.49340945790906,4.49340945790906]\left[-4.49340945790906, 4.49340945790906\right]
Convexa en los intervalos
(−∞,−98.9500628243319]\left(-\infty, -98.9500628243319\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⁡(x))y = \lim_{x \to -\infty}\left(x \cot{\left(x \right)}\right)
True

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