Sr Examen

Otras calculadoras

(-1-sqrt(2)*sqrt(pi)*erf(x*sqrt(2)/2)/2)*exp(x^1)
Trazado el gráfico de la función/ (-1-sqrt(2)*sqrt(pi)*erf(x*sqrt(2)/2)/2)*exp(x^1)

Gráfico de la función y = (-1-sqrt(2)*sqrt(pi)*erf(x*sqrt(2)/2)/2)*exp(x^1)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       /                     /    ___\\      
       |       ___   ____    |x*\/ 2 ||      
       |     \/ 2 *\/ pi *erf|-------||  / 1\
       |                     \   2   /|  \x /
f(x) = |-1 - -------------------------|*e    
       \                 2            /
f(x)=(−2πerf⁡(2x2)2−1)ex1f{\left(x \right)} = \left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}} 
f = (-(sqrt(2)*sqrt(pi))*erf((sqrt(2)*x)/2)/2 - 1)*exp(x^1)
Gráfico de la función
02468-8-6-4-2-1010-10000050000
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:
(−2πerf⁡(2x2)2−1)ex1=0\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=2erfinv⁡(−2π)x_{1} = \sqrt{2} \operatorname{erfinv}{\left(- \frac{\sqrt{2}}{\sqrt{\pi}} \right)}
Solución numérica
x1=−50.8720030830002x_{1} = -50.8720030830002
x2=−44.8720030830002x_{2} = -44.8720030830002
x3=−100.872003083x_{3} = -100.872003083
x4=−108.872003083x_{4} = -108.872003083
x5=−68.8720030830002x_{5} = -68.8720030830002
x6=−116.872003083x_{6} = -116.872003083
x7=−40.8720030830002x_{7} = -40.8720030830002
x8=−48.8720030830002x_{8} = -48.8720030830002
x9=−60.8720030830002x_{9} = -60.8720030830002
x10=−106.872003083x_{10} = -106.872003083
x11=−110.872003083x_{11} = -110.872003083
x12=−38.8720030830002x_{12} = -38.8720030830002
x13=−30.8720030830002x_{13} = -30.8720030830002
x14=−26.8720032139002x_{14} = -26.8720032139002
x15=−118.872003083x_{15} = -118.872003083
x16=−82.8720030830002x_{16} = -82.8720030830002
x17=−66.8720030830002x_{17} = -66.8720030830002
x18=−72.8720030830002x_{18} = -72.8720030830002
x19=−92.8720030830002x_{19} = -92.8720030830002
x20=−90.8720030830002x_{20} = -90.8720030830002
x21=−52.8720030830002x_{21} = -52.8720030830002
x22=−114.872003083x_{22} = -114.872003083
x23=−36.8720030830002x_{23} = -36.8720030830002
x24=−58.8720030830002x_{24} = -58.8720030830002
x25=−80.8720030830002x_{25} = -80.8720030830002
x26=−70.8720030830002x_{26} = -70.8720030830002
x27=−42.8720030830002x_{27} = -42.8720030830002
x28=−102.872003083x_{28} = -102.872003083
x29=−78.8720030830002x_{29} = -78.8720030830002
x30=−56.8720030830002x_{30} = -56.8720030830002
x31=−32.8720030830002x_{31} = -32.8720030830002
x32=−28.8720030830003x_{32} = -28.8720030830003
x33=−46.8720030830002x_{33} = -46.8720030830002
x34=−86.8720030830002x_{34} = -86.8720030830002
x35=−1216.65246823204x_{35} = -1216.65246823204
x36=−1.27554773641722x_{36} = -1.27554773641722
x37=−74.8720030830002x_{37} = -74.8720030830002
x38=−96.8720030830002x_{38} = -96.8720030830002
x39=−64.8720030830002x_{39} = -64.8720030830002
x40=−62.8720030830002x_{40} = -62.8720030830002
x41=−104.872003083x_{41} = -104.872003083
x42=−84.8720030830002x_{42} = -84.8720030830002
x43=−88.8720030830002x_{43} = -88.8720030830002
x44=−98.8720030830002x_{44} = -98.8720030830002
x45=−34.8720030830002x_{45} = -34.8720030830002
x46=−54.8720030830002x_{46} = -54.8720030830002
x47=−94.8720030830002x_{47} = -94.8720030830002
x48=−120.872003083x_{48} = -120.872003083
x49=−76.8720030830002x_{49} = -76.8720030830002
x50=−112.872003083x_{50} = -112.872003083
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 (-1 - (sqrt(2)*sqrt(pi))*erf((x*sqrt(2))/2)/2)*exp(x^1).
(−1−2πerf⁡(022)2)e01\left(-1 - \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{0 \sqrt{2}}{2} \right)}}{2}\right) e^{0^{1}}
Resultado:
f(0)=−1f{\left(0 \right)} = -1
Punto:
(0, -1)
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
(−2πerf⁡(2x2)2−1)ex1−ex1e−x22=0\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}} - e^{x^{1}} e^{- \frac{x^{2}}{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−50.8720030830002x_{1} = -50.8720030830002
x2=−44.8720030830002x_{2} = -44.8720030830002
x3=−100.872003083x_{3} = -100.872003083
x4=−108.872003083x_{4} = -108.872003083
x5=−68.8720030830002x_{5} = -68.8720030830002
x6=−116.872003083x_{6} = -116.872003083
x7=−28.8720030830015x_{7} = -28.8720030830015
x8=−40.8720030830002x_{8} = -40.8720030830002
x9=−48.8720030830002x_{9} = -48.8720030830002
x10=−60.8720030830002x_{10} = -60.8720030830002
x11=−106.872003083x_{11} = -106.872003083
x12=−110.872003083x_{12} = -110.872003083
x13=−38.8720030830002x_{13} = -38.8720030830002
x14=−30.8720030830002x_{14} = -30.8720030830002
x15=−118.872003083x_{15} = -118.872003083
x16=−82.8720030830002x_{16} = -82.8720030830002
x17=−66.8720030830002x_{17} = -66.8720030830002
x18=−72.8720030830002x_{18} = -72.8720030830002
x19=−92.8720030830002x_{19} = -92.8720030830002
x20=−90.8720030830002x_{20} = -90.8720030830002
x21=−52.8720030830002x_{21} = -52.8720030830002
x22=−114.872003083x_{22} = -114.872003083
x23=−36.8720030830002x_{23} = -36.8720030830002
x24=−58.8720030830002x_{24} = -58.8720030830002
x25=−80.8720030830002x_{25} = -80.8720030830002
x26=−70.8720030830002x_{26} = -70.8720030830002
x27=−42.8720030830002x_{27} = -42.8720030830002
x28=−102.872003083x_{28} = -102.872003083
x29=−78.8720030830002x_{29} = -78.8720030830002
x30=−56.8720030830002x_{30} = -56.8720030830002
x31=−32.8720030830002x_{31} = -32.8720030830002
x32=−86.8720030830002x_{32} = -86.8720030830002
x33=−46.8720030830002x_{33} = -46.8720030830002
x34=−74.8720030830002x_{34} = -74.8720030830002
x35=−96.8720030830002x_{35} = -96.8720030830002
x36=−64.8720030830002x_{36} = -64.8720030830002
x37=−62.8720030830002x_{37} = -62.8720030830002
x38=−26.8720039808072x_{38} = -26.8720039808072
x39=−1.86558625786572x_{39} = -1.86558625786572
x40=−84.8720030830002x_{40} = -84.8720030830002
x41=−104.872003083x_{41} = -104.872003083
x42=−88.8720030830002x_{42} = -88.8720030830002
x43=−98.8720030830002x_{43} = -98.8720030830002
x44=−34.8720030830002x_{44} = -34.8720030830002
x45=−54.8720030830002x_{45} = -54.8720030830002
x46=−94.8720030830002x_{46} = -94.8720030830002
x47=−120.872003083x_{47} = -120.872003083
x48=−76.8720030830002x_{48} = -76.8720030830002
x49=−112.872003083x_{49} = -112.872003083
Signos de extremos en los puntos:
                                                                     ___   ____    /                   ___\ 
(-50.872003083000195, -8.06435760224971e-23 + 4.03217880112485e-23*\/ 2 *\/ pi *erf\25.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-44.872003083000195, -3.25339405776957e-20 + 1.62669702888478e-20*\/ 2 *\/ pi *erf\22.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-100.8720030830002, -1.55541284992658e-44 + 7.77706424963289e-45*\/ 2 *\/ pi *erf\50.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-108.8720030830002, -5.21782882109705e-48 + 2.60891441054853e-48*\/ 2 *\/ pi *erf\54.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-68.8720030830002, -1.22820002936382e-30 + 6.14100014681912e-31*\/ 2 *\/ pi *erf\34.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-116.8720030830002, -1.75038656827068e-51 + 8.75193284135341e-52*\/ 2 *\/ pi *erf\58.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-28.87200308300149, -2.89100191640664e-13 + 1.44550095820332e-13*\/ 2 *\/ pi *erf\14.4360015415007*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-40.872003083000195, -1.77629296883043e-18 + 8.88146484415213e-19*\/ 2 *\/ pi *erf\20.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-48.872003083000195, -5.95879907248609e-22 + 2.97939953624305e-22*\/ 2 *\/ pi *erf\24.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-60.872003083000195, -3.66121268721697e-27 + 1.83060634360849e-27*\/ 2 *\/ pi *erf\30.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-106.8720030830002, -3.85548298737033e-47 + 1.92774149368517e-47*\/ 2 *\/ pi *erf\53.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-110.8720030830002, -7.06156341383331e-49 + 3.53078170691665e-49*\/ 2 *\/ pi *erf\55.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-38.872003083000195, -1.31251283948241e-17 + 6.56256419741205e-18*\/ 2 *\/ pi *erf\19.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-30.87200308300019, -3.91254563194992e-14 + 1.95627281597496e-14*\/ 2 *\/ pi *erf\15.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-118.8720030830002, -2.36889061990475e-52 + 1.18444530995238e-52*\/ 2 *\/ pi *erf\59.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-82.8720030830002, -1.02128359721986e-36 + 5.10641798609932e-37*\/ 2 *\/ pi *erf\41.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-66.8720030830002, -9.07523891767756e-30 + 4.53761945883878e-30*\/ 2 *\/ pi *erf\33.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-72.8720030830002, -2.24952682209605e-32 + 1.12476341104803e-32*\/ 2 *\/ pi *erf\36.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-92.8720030830002, -4.63662035813597e-41 + 2.31831017906799e-41*\/ 2 *\/ pi *erf\46.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-90.8720030830002, -3.42602479357106e-40 + 1.71301239678553e-40*\/ 2 *\/ pi *erf\45.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-52.872003083000195, -1.09139212022179e-23 + 5.45696060110897e-24*\/ 2 *\/ pi *erf\26.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-114.8720030830002, -1.29337045477668e-50 + 6.46685227388339e-51*\/ 2 *\/ pi *erf\57.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-36.872003083000195, -9.69823100150228e-17 + 4.84911550075114e-17*\/ 2 *\/ pi *erf\18.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-58.872003083000195, -2.70529059359629e-26 + 1.35264529679814e-26*\/ 2 *\/ pi *erf\29.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-80.8720030830002, -7.54632179277527e-36 + 3.77316089638764e-36*\/ 2 *\/ pi *erf\40.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-70.8720030830002, -1.66218798845169e-31 + 8.31093994225845e-32*\/ 2 *\/ pi *erf\35.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-42.872003083000195, -2.40395112047869e-19 + 1.20197556023935e-19*\/ 2 *\/ pi *erf\21.4360015415001*\/ 2 /)

                                                                  ___   ____    /                   ___\ 
(-102.8720030830002, -2.1050223859468e-45 + 1.0525111929734e-45*\/ 2 *\/ pi *erf\51.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-78.8720030830002, -5.57601950673994e-35 + 2.78800975336997e-35*\/ 2 *\/ pi *erf\39.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-56.872003083000195, -1.99895439599924e-25 + 9.99477197999618e-26*\/ 2 *\/ pi *erf\28.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-32.872003083000195, -5.29505471276112e-15 + 2.64752735638056e-15*\/ 2 *\/ pi *erf\16.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-86.8720030830002, -1.87054615696665e-38 + 9.35273078483324e-39*\/ 2 *\/ pi *erf\43.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-46.872003083000195, -4.40299006288557e-21 + 2.20149503144278e-21*\/ 2 *\/ pi *erf\23.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-74.8720030830002, -3.04440349616726e-33 + 1.52220174808363e-33*\/ 2 *\/ pi *erf\37.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-96.8720030830002, -8.49226641437718e-43 + 4.24613320718859e-43*\/ 2 *\/ pi *erf\48.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-64.8720030830002, -6.70574494739182e-29 + 3.35287247369591e-29*\/ 2 *\/ pi *erf\32.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-62.872003083000195, -4.95491256013989e-28 + 2.47745628006995e-28*\/ 2 *\/ pi *erf\31.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-26.872003980807204, -2.13617561637294e-12 + 1.06808780818647e-12*\/ 2 *\/ pi *erf\13.4360019904036*\/ 2 /)

                                                                ___   ____    /                    ___\ 
(-1.8655862578657156, -0.154805427377072 + 0.0774027136885361*\/ 2 *\/ pi *erf\0.932793128932858*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-84.8720030830002, -1.38215704894657e-37 + 6.91078524473285e-38*\/ 2 *\/ pi *erf\42.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-104.8720030830002, -2.84883800821521e-46 + 1.42441900410761e-46*\/ 2 *\/ pi *erf\52.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-88.8720030830002, -2.53150893960239e-39 + 1.26575446980119e-39*\/ 2 *\/ pi *erf\44.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-98.8720030830002, -1.14930328051051e-43 + 5.74651640255255e-44*\/ 2 *\/ pi *erf\49.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-34.872003083000195, -7.16607729304888e-16 + 3.58303864652444e-16*\/ 2 *\/ pi *erf\17.4360015415001*\/ 2 /)

                                                                     ___   ____    /                   ___\ 
(-54.872003083000195, -1.47703861712424e-24 + 7.38519308562119e-25*\/ 2 *\/ pi *erf\27.4360015415001*\/ 2 /)

                                                                   ___   ____    /                   ___\ 
(-94.8720030830002, -6.27498329428976e-42 + 3.13749164714488e-42*\/ 2 *\/ pi *erf\47.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-120.8720030830002, -3.20594483001365e-53 + 1.60297241500682e-53*\/ 2 *\/ pi *erf\60.4360015415001*\/ 2 /)

                                                                  ___   ____    /                   ___\ 
(-76.8720030830002, -4.1201520944033e-34 + 2.06007604720165e-34*\/ 2 *\/ pi *erf\38.4360015415001*\/ 2 /)

                                                                    ___   ____    /                   ___\ 
(-112.8720030830002, -9.55678684704432e-50 + 4.77839342352216e-50*\/ 2 *\/ pi *erf\56.4360015415001*\/ 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:
x49=−1.86558625786572x_{49} = -1.86558625786572
Decrece en los intervalos
(−∞,−1.86558625786572]\left(-\infty, -1.86558625786572\right]
Crece en los intervalos
[−1.86558625786572,∞)\left[-1.86558625786572, \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
(xe−x22−2πerf⁡(2x2)2−1−2e−x22)ex1=0\left(x e^{- \frac{x^{2}}{2}} - \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1 - 2 e^{- \frac{x^{2}}{2}}\right) e^{x^{1}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−50.8720030830002x_{1} = -50.8720030830002
x2=−44.8720030830002x_{2} = -44.8720030830002
x3=−2.42452381454183x_{3} = -2.42452381454183
x4=−108.872003083x_{4} = -108.872003083
x5=−100.872003083x_{5} = -100.872003083
x6=−68.8720030830002x_{6} = -68.8720030830002
x7=−116.872003083x_{7} = -116.872003083
x8=−40.8720030830002x_{8} = -40.8720030830002
x9=−48.8720030830002x_{9} = -48.8720030830002
x10=−60.8720030830002x_{10} = -60.8720030830002
x11=−106.872003083x_{11} = -106.872003083
x12=−110.872003083x_{12} = -110.872003083
x13=−38.8720030830002x_{13} = -38.8720030830002
x14=−30.8720030830002x_{14} = -30.8720030830002
x15=−26.8720091111952x_{15} = -26.8720091111952
x16=−118.872003083x_{16} = -118.872003083
x17=−82.8720030830002x_{17} = -82.8720030830002
x18=−66.8720030830002x_{18} = -66.8720030830002
x19=−72.8720030830002x_{19} = -72.8720030830002
x20=−92.8720030830002x_{20} = -92.8720030830002
x21=−90.8720030830002x_{21} = -90.8720030830002
x22=−52.8720030830002x_{22} = -52.8720030830002
x23=−114.872003083x_{23} = -114.872003083
x24=−36.8720030830002x_{24} = -36.8720030830002
x25=−2.42452381454184x_{25} = -2.42452381454184
x26=−58.8720030830002x_{26} = -58.8720030830002
x27=−80.8720030830002x_{27} = -80.8720030830002
x28=−70.8720030830002x_{28} = -70.8720030830002
x29=−42.8720030830002x_{29} = -42.8720030830002
x30=−102.872003083x_{30} = -102.872003083
x31=−78.8720030830002x_{31} = -78.8720030830002
x32=−56.8720030830002x_{32} = -56.8720030830002
x33=−32.8720030830002x_{33} = -32.8720030830002
x34=−86.8720030830002x_{34} = -86.8720030830002
x35=−46.8720030830002x_{35} = -46.8720030830002
x36=−74.8720030830002x_{36} = -74.8720030830002
x37=−28.8720030830115x_{37} = -28.8720030830115
x38=−96.8720030830002x_{38} = -96.8720030830002
x39=−64.8720030830002x_{39} = -64.8720030830002
x40=−62.8720030830002x_{40} = -62.8720030830002
x41=−104.872003083x_{41} = -104.872003083
x42=−84.8720030830002x_{42} = -84.8720030830002
x43=−88.8720030830002x_{43} = -88.8720030830002
x44=−98.8720030830002x_{44} = -98.8720030830002
x45=−34.8720030830002x_{45} = -34.8720030830002
x46=−54.8720030830002x_{46} = -54.8720030830002
x47=−94.8720030830002x_{47} = -94.8720030830002
x48=−120.872003083x_{48} = -120.872003083
x49=−76.8720030830002x_{49} = -76.8720030830002
x50=−112.872003083x_{50} = -112.872003083

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
(−∞,−2.42452381454184]\left(-\infty, -2.42452381454184\right]
Convexa en los intervalos
[−2.42452381454183,∞)\left[-2.42452381454183, \infty\right)
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((−2πerf⁡(2x2)2−1)ex1)=0\lim_{x \to -\infty}\left(\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞((−2πerf⁡(2x2)2−1)ex1)=−∞\lim_{x \to \infty}\left(\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}}\right) = -\infty
Tomamos como el límite
es decir,
no hay asíntota horizontal a la derecha
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (-1 - (sqrt(2)*sqrt(pi))*erf((x*sqrt(2))/2)/2)*exp(x^1), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((−2πerf⁡(2x2)2−1)ex1x)=0\lim_{x \to -\infty}\left(\frac{\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞((−2πerf⁡(2x2)2−1)ex1x)=−∞\lim_{x \to \infty}\left(\frac{\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}}}{x}\right) = -\infty
Tomamos como el límite
es decir,
no hay asíntota inclinada a la derecha
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:
(−2πerf⁡(2x2)2−1)ex1=(2πerf⁡(2x2)2−1)e−x\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}} = \left(\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{- x}
- No
(−2πerf⁡(2x2)2−1)ex1=−(2πerf⁡(2x2)2−1)e−x\left(- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{x^{1}} = - \left(\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - 1\right) e^{- x}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = (-1-sqrt(2)*sqrt(pi)*erf(x*sqrt(2)/2)/2)*exp(x^1)
    © Sr Examen – Калькулятор