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Trazado el gráfico de la función/ (-1+(-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)*exp(-x)/25)*exp(x)

Gráfico de la función y = (-1+(-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)*exp(-x)/25)*exp(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       /                                                                2  -x\   
       |     (-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*e *e  |  x
f(x) = |-1 + ----------------------------------------------------------------|*e 
       \                                    25                               /
f(x)=((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)exf{\left(x \right)} = \left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x} 
f = ((((-5*x*sin(2*x) - 10*x*cos(2*x) + 3*sin(2*x) - 4*cos(2*x))*exp(2))*exp(-x))/25 - 1)*exp(x)
Gráfico de la función
02468-8-6-4-2-1010-2500025000
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:
((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex=0\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−6.80649805545073x_{1} = -6.80649805545073
x2=−30.392080701905x_{2} = -30.392080701905
x3=−38.2474297987677x_{3} = -38.2474297987677
x4=−33.5342976831179x_{4} = -33.5342976831179
x5=−11.5315061987173x_{5} = -11.5315061987173
x6=−82.2325453148142x_{6} = -82.2325453148142
x7=−9.95786677190331x_{7} = -9.95786677190331
x8=−91.6575745206459x_{8} = -91.6575745206459
x9=−16.2490784306785x_{9} = -16.2490784306785
x10=−99.5117290970474x_{10} = -99.5117290970474
x11=−93.2284077721128x_{11} = -93.2284077721128
x12=−55.5278310424106x_{12} = -55.5278310424106
x13=−5.2264184782404x_{13} = -5.2264184782404
x14=−71.2365936441077x_{14} = -71.2365936441077
x15=−75.9491577762104x_{15} = -75.9491577762104
x16=−69.6657336523285x_{16} = -69.6657336523285
x17=−27.2497186610371x_{17} = -27.2497186610371
x18=−2.02727123503204x_{18} = -2.02727123503204
x19=−17.8209857999767x_{19} = -17.8209857999767
x20=−97.9409004053142x_{20} = -97.9409004053142
x21=−8.38313915573687x_{21} = -8.38313915573687
x22=−63.3822620275935x_{22} = -63.3822620275935
x23=−31.9632046337359x_{23} = -31.9632046337359
x24=−25.6784664664366x_{24} = -25.6784664664366
x25=−53.9569290879675x_{25} = -53.9569290879675
x26=−61.8113849962171x_{26} = -61.8113849962171
x27=−47.6732513637146x_{27} = -47.6732513637146
x28=−96.3700706562873x_{28} = -96.3700706562873
x29=−90.0867399786036x_{29} = -90.0867399786036
x30=−3.63606896972874x_{30} = -3.63606896972874
x31=−46.1023108671164x_{31} = -46.1023108671164
x32=−49.2441826243389x_{32} = -49.2441826243389
x33=−85.3742278949593x_{33} = -85.3742278949593
x34=−60.2405037417412x_{34} = -60.2405037417412
x35=−52.3860207742208x_{35} = -52.3860207742208
x36=−83.8033874497159x_{36} = -83.8033874497159
x37=−77.52000774231x_{37} = -77.52000774231
x38=−39.8184345452483x_{38} = -39.8184345452483
x39=−68.0948707145325x_{39} = -68.0948707145325
x40=1.88419333234993x_{40} = 1.88419333234993
x41=−41.3894233927615x_{41} = -41.3894233927615
x42=−24.1071543447117x_{42} = -24.1071543447117
x43=−88.5159040771196x_{43} = -88.5159040771196
x44=−74.3783055382886x_{44} = -74.3783055382886
x45=−19.3927111661575x_{45} = -19.3927111661575
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 + (((-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*exp(2))*exp(-x))/25)*exp(x).
((((−4cos⁡(0⋅2)+3sin⁡(0⋅2))−0⋅10cos⁡(0⋅2))−0⋅5sin⁡(0⋅2))e2e−025−1)e0\left(\frac{\left(\left(\left(- 4 \cos{\left(0 \cdot 2 \right)} + 3 \sin{\left(0 \cdot 2 \right)}\right) - 0 \cdot 10 \cos{\left(0 \cdot 2 \right)}\right) - 0 \cdot 5 \sin{\left(0 \cdot 2 \right)}\right) e^{2} e^{- 0}}{25} - 1\right) e^{0}
Resultado:
f(0)=−4e225−1f{\left(0 \right)} = - \frac{4 e^{2}}{25} - 1
Punto:
(0, -1 - 4*exp(2)/25)
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
((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex+(−(−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25+(20xsin⁡(2x)−10xcos⁡(2x)+3sin⁡(2x)−4cos⁡(2x))e2e−x25)ex=0\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x} + \left(- \frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} + \frac{\left(20 x \sin{\left(2 x \right)} - 10 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2} e^{- x}}{25}\right) e^{x} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−86.1625558175537x_{1} = -86.1625558175537
x2=−42.180868035436x_{2} = -42.180868035436
x3=−26.4736167915785x_{3} = -26.4736167915785
x4=−23.332282565423x_{4} = -23.332282565423
x5=−59.4592803626043x_{5} = -59.4592803626043
x6=−87.7333417066779x_{6} = -87.7333417066779
x7=−122.290699217015x_{7} = -122.290699217015
x8=−37.4686296462638x_{8} = -37.4686296462638
x9=−95.5872763087217x_{9} = -95.5872763087217
x10=0.485642591920839x_{10} = 0.485642591920839
x11=−12.3386658128028x_{11} = -12.3386658128028
x12=−20.1910295447758x_{12} = -20.1910295447758
x13=−81.4502005716198x_{13} = -81.4502005716198
x14=−50.0346619693212x_{14} = -50.0346619693212
x15=−72.0255033591792x_{15} = -72.0255033591792
x16=−92.4457015068628x_{16} = -92.4457015068628
x17=−51.6054276384411x_{17} = -51.6054276384411
x18=−21.7616436866747x_{18} = -21.7616436866747
x19=−7.62888295899474x_{19} = -7.62888295899474
x20=−35.8978923510335x_{20} = -35.8978923510335
x21=−64.1716071901995x_{21} = -64.1716071901995
x22=−28.0443057693738x_{22} = -28.0443057693738
x23=−15.4794117949441x_{23} = -15.4794117949441
x24=−1.36525791181951x_{24} = -1.36525791181951
x25=−65.742384785425x_{25} = -65.742384785425
x26=−67.3131632574602x_{26} = -67.3131632574602
x27=−29.6150062107158x_{27} = -29.6150062107158
x28=−0.356377966067794x_{28} = -0.356377966067794
x29=−56.3177349431024x_{29} = -56.3177349431024
x30=−34.3271604895018x_{30} = -34.3271604895018
x31=1.61431420148329x_{31} = 1.61431420148329
x32=−4.49201527484935x_{32} = -4.49201527484935
x33=−13.9089903085589x_{33} = -13.9089903085589
x34=−57.8885070098078x_{34} = -57.8885070098078
x35=−43.7516214066214x_{35} = -43.7516214066214
x36=−78.308632669004x_{36} = -78.308632669004
x37=−94.0164887583458x_{37} = -94.0164887583458
x38=−48.46389829568x_{38} = -48.46389829568
x39=−100.2996406125x_{39} = -100.2996406125
x40=−79.8794163763463x_{40} = -79.8794163763463
x41=−6.05992334565186x_{41} = -6.05992334565186
x42=−89.3041279638035x_{42} = -89.3041279638035
x43=−70.4547225967174x_{43} = -70.4547225967174
x44=−45.3223777683704x_{44} = -45.3223777683704
x45=−73.5962847878296x_{45} = -73.5962847878296
Signos de extremos en los puntos:
                                                              2 
(-86.1625558175537, -3.80257213817311e-38 - 38.4433895566568*e )

                                                               2 
(-42.18086803543602, -4.79823782852017e-19 - 18.7739355619817*e )

                                                               2 
(-26.473616791578536, -3.18166398083337e-12 - 11.749152675255*e )

                                                                2 
(-23.332282565423004, -7.36068837450199e-11 - 10.3442012872768*e )

                                                               2 
(-59.45928036260429, -1.50370498882589e-26 + 26.5012162355076*e )

                                                               2 
(-87.73334170667792, -7.90485335909186e-39 + 39.1458705629708*e )

                                                               2 
(-122.2906992170149, -7.75932855988518e-54 + 54.6004557407121*e )

                                                               2 
(-37.46862964626381, -5.34048746632774e-17 + 16.6664978775403*e )

                                                              2 
(-95.58727630872174, -3.06883373035186e-42 - 42.658275825146*e )

                                                            2 
(0.4856425919208386, -1.62521902598551 - 0.181002653785227*e )

                                                               2 
(-12.338665812802816, -4.37910666210048e-6 + 5.42691853666758*e )

                                                              2 
(-20.19102954477579, -1.70273586898973e-9 - 8.93925353165252*e )

                                                               2 
(-81.45020057161976, -4.23279603623058e-36 + 36.3359466460064*e )

                                                              2 
(-50.0346619693212, -1.86304095837176e-22 + 22.2863345330862*e )

                                                               2 
(-72.02550335917921, -5.24470825384584e-32 + 32.1210614185897*e )

                                                               2 
(-92.44570150686276, -7.10136703669347e-41 - 41.2533136772963*e )

                                                               2 
(-51.60542763844109, -3.87300038687144e-23 - 22.9888146351093*e )

                                                               2 
(-21.76164368667469, -3.54028503854004e-10 + 9.64172685620577*e )

                                                              2 
(-7.628882958994735, -0.00048620366454576 - 3.31959096270077*e )

                                                              2 
(-35.89789235103348, -2.5688777666601e-16 - 15.9640190445123*e )

                                                              2 
(-64.17160719019948, -1.35090591241632e-28 - 28.608657875224*e )

                                                             2 
(-28.04430576937379, -6.6147396518336e-13 + 12.451629347221*e )

                                                              2 
(-15.479411794944113, -1.89398647925637e-7 + 6.8318436088485*e )

                                                              2 
(-1.3652579118195132, -0.255314818786306 - 0.510999425397725*e )

                                                              2 
(-65.74238478542499, -2.8083100911911e-29 + 29.3111385106163*e )

                                                              2 
(-67.3131632574602, -5.83800735547156e-30 - 30.0136191852217*e )

                                                                2 
(-29.615006210715844, -1.37520113195543e-13 - 13.1541065319221*e )

                                                              2 
(-0.3563779660677943, -0.700207915381262 - 0.138280301623535*e )

                                                              2 
(-56.3177349431024, -3.47951314016858e-25 + 25.0962554017054*e )

                                                               2 
(-34.32716048950175, -1.23567317853403e-15 + 15.2615404545068*e )

                                                            2 
(1.6143142014832885, -5.02444098747554 + 0.820309867290977*e )

                                                            2 
(-4.49201527484935, -0.0111980538984115 - 1.91484815364418*e )

                                                              2 
(-13.90899030855889, -9.10756459516233e-7 - 6.12937890360175*e )

                                                               2 
(-57.888507009807775, -7.2333726549911e-26 - 25.7987357898477*e )

                                                               2 
(-43.75162140662138, -9.97498494258532e-20 + 19.4764151139974*e )

                                                               2 
(-78.30863266900396, -9.79474077279153e-35 + 34.9309848067047*e )

                                                          2 
(-94.0164887583458, -1.4762425684e-41 + 41.9557947445376*e )

                                                                2 
(-48.463898295680046, -8.96182375347277e-22 - 21.5838545203074*e )

                                                                2 
(-100.29964061249967, -2.75689067938869e-44 + 44.7657191408808*e )

                                                               2 
(-79.87941637634631, -2.03615225727808e-35 - 35.6334657154449*e )

                                                              2 
(-6.059923345651865, -0.00233457983636597 + 2.61719015732254*e )

                                                               2 
(-89.30412796380352, -1.64327411454649e-39 - 39.8483515857425*e )

                                                              2 
(-70.45472259671737, -2.52291577468178e-31 - 31.418580641551*e )

                                                                2 
(-45.322377768370444, -2.07367851697082e-20 - 20.1788947997625*e )

                                                               2 
(-73.59628478782957, -1.09028397298003e-32 - 32.8235422254219*e )


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:
Puntos mínimos de la función:
x1=−86.1625558175537x_{1} = -86.1625558175537
x2=−42.180868035436x_{2} = -42.180868035436
x3=−26.4736167915785x_{3} = -26.4736167915785
x4=−23.332282565423x_{4} = -23.332282565423
x5=−95.5872763087217x_{5} = -95.5872763087217
x6=0.485642591920839x_{6} = 0.485642591920839
x7=−20.1910295447758x_{7} = -20.1910295447758
x8=−92.4457015068628x_{8} = -92.4457015068628
x9=−51.6054276384411x_{9} = -51.6054276384411
x10=−7.62888295899474x_{10} = -7.62888295899474
x11=−35.8978923510335x_{11} = -35.8978923510335
x12=−64.1716071901995x_{12} = -64.1716071901995
x13=−1.36525791181951x_{13} = -1.36525791181951
x14=−67.3131632574602x_{14} = -67.3131632574602
x15=−29.6150062107158x_{15} = -29.6150062107158
x16=−4.49201527484935x_{16} = -4.49201527484935
x17=−13.9089903085589x_{17} = -13.9089903085589
x18=−57.8885070098078x_{18} = -57.8885070098078
x19=−48.46389829568x_{19} = -48.46389829568
x20=−79.8794163763463x_{20} = -79.8794163763463
x21=−89.3041279638035x_{21} = -89.3041279638035
x22=−70.4547225967174x_{22} = -70.4547225967174
x23=−45.3223777683704x_{23} = -45.3223777683704
x24=−73.5962847878296x_{24} = -73.5962847878296
Puntos máximos de la función:
x24=−59.4592803626043x_{24} = -59.4592803626043
x24=−87.7333417066779x_{24} = -87.7333417066779
x24=−122.290699217015x_{24} = -122.290699217015
x24=−37.4686296462638x_{24} = -37.4686296462638
x24=−12.3386658128028x_{24} = -12.3386658128028
x24=−81.4502005716198x_{24} = -81.4502005716198
x24=−50.0346619693212x_{24} = -50.0346619693212
x24=−72.0255033591792x_{24} = -72.0255033591792
x24=−21.7616436866747x_{24} = -21.7616436866747
x24=−28.0443057693738x_{24} = -28.0443057693738
x24=−15.4794117949441x_{24} = -15.4794117949441
x24=−65.742384785425x_{24} = -65.742384785425
x24=−0.356377966067794x_{24} = -0.356377966067794
x24=−56.3177349431024x_{24} = -56.3177349431024
x24=−34.3271604895018x_{24} = -34.3271604895018
x24=1.61431420148329x_{24} = 1.61431420148329
x24=−43.7516214066214x_{24} = -43.7516214066214
x24=−78.308632669004x_{24} = -78.308632669004
x24=−94.0164887583458x_{24} = -94.0164887583458
x24=−100.2996406125x_{24} = -100.2996406125
x24=−6.05992334565186x_{24} = -6.05992334565186
Decrece en los intervalos
[0.485642591920839,∞)\left[0.485642591920839, \infty\right)
Crece en los intervalos
(−∞,−95.5872763087217]\left(-\infty, -95.5872763087217\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
2xe2sin⁡(2x)−((5xsin⁡(2x)+10xcos⁡(2x)−3sin⁡(2x)+4cos⁡(2x))e2e−x+25)ex25+(−xsin⁡(2x)+2xcos⁡(2x)+sin⁡(2x))e2=02 x e^{2} \sin{\left(2 x \right)} - \frac{\left(\left(5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}\right) e^{2} e^{- x} + 25\right) e^{x}}{25} + \left(- x \sin{\left(2 x \right)} + 2 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) e^{2} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−97.9460157604398x_{1} = -97.9460157604398
x2=−2.26399247540341x_{2} = -2.26399247540341
x3=−93.2337822301932x_{3} = -93.2337822301932
x4=−90.0923022635643x_{4} = -90.0923022635643
x5=−3.77846745542346x_{5} = -3.77846745542346
x6=−16.2801854772586x_{6} = -16.2801854772586
x7=−25.6980790089547x_{7} = -25.6980790089547
x8=−82.2386401004529x_{8} = -82.2386401004529
x9=−17.8493252269748x_{9} = -17.8493252269748
x10=−60.2488305449496x_{10} = -60.2488305449496
x11=−49.2543758469485x_{11} = -49.2543758469485
x12=−85.3800978970367x_{12} = -85.3800978970367
x13=−88.5215652860922x_{13} = -88.5215652860922
x14=−69.6729308591578x_{14} = -69.6729308591578
x15=−27.2681932185021x_{15} = -27.2681932185021
x16=−99.5167635483288x_{16} = -99.5167635483288
x17=−61.8194995387526x_{17} = -61.8194995387526
x18=−91.6630412793407x_{18} = -91.6630412793407
x19=1.14581782989756x_{19} = 1.14581782989756
x20=−71.2436317213696x_{20} = -71.2436317213696
x21=−53.9662289489669x_{21} = -53.9662289489669
x22=−96.3752695579269x_{22} = -96.3752695579269
x23=−6.88154513901669x_{23} = -6.88154513901669
x24=−83.8093677321176x_{24} = -83.8093677321176
x25=−38.2605677226714x_{25} = -38.2605677226714
x26=−41.4015596186877x_{26} = -41.4015596186877
x27=−63.3901748615295x_{27} = -63.3901748615295
x28=−39.8310517723009x_{28} = -39.8310517723009
x29=−8.44388158097994x_{29} = -8.44388158097994
x30=−33.54929194441x_{30} = -33.54929194441
x31=−77.5264739484552x_{31} = -77.5264739484552
x32=−74.3850455717934x_{32} = -74.3850455717934
x33=−55.5368669248221x_{33} = -55.5368669248221
x34=−68.102234412857x_{34} = -68.102234412857
x35=−47.6837817731732x_{35} = -47.6837817731732
x36=−46.1132015324485x_{36} = -46.1132015324485
x37=−75.9557580572675x_{37} = -75.9557580572675
x38=−30.4086341979852x_{38} = -30.4086341979852
x39=−10.0088989055393x_{39} = -10.0088989055393
x40=3.76055097997223x_{40} = 3.76055097997223
x41=−11.5754966745279x_{41} = -11.5754966745279
x42=0.077328935865687x_{42} = 0.077328935865687
x43=−31.9789399874986x_{43} = -31.9789399874986
x44=−24.1280542185133x_{44} = -24.1280542185133
x45=−5.32420786956144x_{45} = -5.32420786956144
x46=−52.39560050084x_{46} = -52.39560050084
x47=−19.4187349803007x_{47} = -19.4187349803007

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
[0.077328935865687,∞)\left[0.077328935865687, \infty\right)
Convexa en los intervalos
(−∞,−99.5167635483288]\left(-\infty, -99.5167635483288\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→−∞(((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex)y = \lim_{x \to -\infty}\left(\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x}\right)
lim⁡x→∞(((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex)=−∞\lim_{x \to \infty}\left(\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x}\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 + (((-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*exp(2))*exp(-x))/25)*exp(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→−∞(((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)exx)y = x \lim_{x \to -\infty}\left(\frac{\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x}}{x}\right)
lim⁡x→∞(((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)exx)=−∞\lim_{x \to \infty}\left(\frac{\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x}}{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:
((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex=((−5xsin⁡(2x)+10xcos⁡(2x)−3sin⁡(2x)−4cos⁡(2x))e2ex25−1)e−x\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x} = \left(\frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2} e^{x}}{25} - 1\right) e^{- x}
- No
((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e2e−x25−1)ex=−((−5xsin⁡(2x)+10xcos⁡(2x)−3sin⁡(2x)−4cos⁡(2x))e2ex25−1)e−x\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2} e^{- x}}{25} - 1\right) e^{x} = - \left(\frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2} e^{x}}{25} - 1\right) e^{- x}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор