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Trazado el gráfico de la función/ (sin(pi-x^2))+(cos*x)

Gráfico de la función y = (sin(pi-x^2))+(cos*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          /      2\         
f(x) = sin\pi - x / + cos(x)
f(x)=sin⁡(π−x2)+cos⁡(x)f{\left(x \right)} = \sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)} 
f = sin(pi - x^2) + cos(x)
Gráfico de la función
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.05-5
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:
sin⁡(π−x2)+cos⁡(x)=0\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=39.3537963861618x_{1} = 39.3537963861618
x2=14.703850171547x_{2} = 14.703850171547
x3=−89.5043587473482x_{3} = -89.5043587473482
x4=90.2866638151927x_{4} = 90.2866638151927
x5=−66.2812905817993x_{5} = -66.2812905817993
x6=62.1551675495361x_{6} = 62.1551675495361
x7=25.6650734093573x_{7} = 25.6650734093573
x8=41.2887645078372x_{8} = 41.2887645078372
x9=82.2487231834966x_{9} = 82.2487231834966
x10=56.372837425881x_{10} = 56.372837425881
x11=52.5262632818042x_{11} = 52.5262632818042
x12=−70.1669054287859x_{12} = -70.1669054287859
x13=−45.8131415719649x_{13} = -45.8131415719649
x14=96.2384278482168x_{14} = 96.2384278482168
x15=−71.7496103376305x_{15} = -71.7496103376305
x16=−184.308210135539x_{16} = -184.308210135539
x17=−35.8416620973313x_{17} = -35.8416620973313
x18=77.3022799603946x_{18} = 77.3022799603946
x19=44.2550591180873x_{19} = 44.2550591180873
x20=−12.9803379903228x_{20} = -12.9803379903228
x21=−98.251747073356x_{21} = -98.251747073356
x22=46.3135757647168x_{22} = 46.3135757647168
x23=−1.72764202249479x_{23} = -1.72764202249479
x24=82.4858980700667x_{24} = 82.4858980700667
x25=−92.6774720530418x_{25} = -92.6774720530418
x26=17.6461048961753x_{26} = 17.6461048961753
x27=−32.2582644717469x_{27} = -32.2582644717469
x28=−43.7558484509635x_{28} = -43.7558484509635
x29=52.3054304031407x_{29} = 52.3054304031407
x30=−33.7583545447791x_{30} = -33.7583545447791
x31=−13.8535472553x_{31} = -13.8535472553
x32=68.8656914401692x_{32} = 68.8656914401692
x33=1.72764202249479x_{33} = 1.72764202249479
x34=49.8694954091636x_{34} = 49.8694954091636
x35=14.4957952350541x_{35} = 14.4957952350541
x36=−67.7240391379261x_{36} = -67.7240391379261
x37=−133.25170051759x_{37} = -133.25170051759
x38=−58.0318855988299x_{38} = -58.0318855988299
x39=91.1134780270404x_{39} = 91.1134780270404
x40=92.1819564837024x_{40} = 92.1819564837024
x41=−22.307533495955x_{41} = -22.307533495955
x42=8.10682446430506x_{42} = 8.10682446430506
x43=−21.7497380420623x_{43} = -21.7497380420623
x44=−75.8570084422381x_{44} = -75.8570084422381
x45=−41.7268141222163x_{45} = -41.7268141222163
x46=−37.4975239235994x_{46} = -37.4975239235994
x47=−14.1811828029814x_{47} = -14.1811828029814
x48=−12.2295727210254x_{48} = -12.2295727210254
x49=−30.557576214776x_{49} = -30.557576214776
x50=65.9984335148403x_{50} = 65.9984335148403
x51=−55.6501400521616x_{51} = -55.6501400521616
x52=24.2521763491131x_{52} = 24.2521763491131
x53=54.2489018025096x_{53} = 54.2489018025096
x54=80.4685053404278x_{54} = 80.4685053404278
x55=−99.7585442501563x_{55} = -99.7585442501563
x56=−79.6646915600498x_{56} = -79.6646915600498
x57=47.179165644477x_{57} = 47.179165644477
x58=−91.1481416547747x_{58} = -91.1481416547747
x59=74.1449232777521x_{59} = 74.1449232777521
x60=−9.77099575967482x_{60} = -9.77099575967482
x61=58.2498969850645x_{61} = 58.2498969850645
x62=98.2430139322065x_{62} = 98.2430139322065
x63=64.3238395513282x_{63} = 64.3238395513282
x64=−85.2740714787644x_{64} = -85.2740714787644
x65=82.6007736764819x_{65} = 82.6007736764819
x66=31.5799250942183x_{66} = 31.5799250942183
x67=−18.1872402887557x_{67} = -18.1872402887557
x68=−59.7524714117438x_{68} = -59.7524714117438
x69=−7.73372589124635x_{69} = -7.73372589124635
x70=2.72764202249479x_{70} = 2.72764202249479
x71=−38.3963605328762x_{71} = -38.3963605328762
x72=−59.9123669475315x_{72} = -59.9123669475315
x73=94.2488957183894x_{73} = 94.2488957183894
x74=84.3481559357716x_{74} = 84.3481559357716
x75=−93.7502160635462x_{75} = -93.7502160635462
x76=14.8535472553x_{76} = 14.8535472553
x77=31.382411990719x_{77} = 31.382411990719
x78=−23.2521763491131x_{78} = -23.2521763491131
x79=−81.7154887730921x_{79} = -81.7154887730921
x80=5.98590286179978x_{80} = 5.98590286179978
x81=−45.4651517576115x_{81} = -45.4651517576115
x82=−62.9039589619485x_{82} = -62.9039589619485
x83=−5.98590286179978x_{83} = -5.98590286179978
x84=24.7754736832896x_{84} = 24.7754736832896
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(pi - x^2) + cos(x).
sin⁡(π−02)+cos⁡(0)\sin{\left(\pi - 0^{2} \right)} + \cos{\left(0 \right)}
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
2xcos⁡(x2)−sin⁡(x)=02 x \cos{\left(x^{2} \right)} - \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=70.1519690117632x_{1} = 70.1519690117632
x2=−5.45689420149144x_{2} = -5.45689420149144
x3=98.4390519310906x_{3} = 98.4390519310906
x4=60.2503601843957x_{4} = 60.2503601843957
x5=16.000961718966x_{5} = 16.000961718966
x6=−9.29520030332014x_{6} = -9.29520030332014
x7=−19.2131827846554x_{7} = -19.2131827846554
x8=−68.2452687572932x_{8} = -68.2452687572932
x9=90.2124794543957x_{9} = 90.2124794543957
x10=−23.8133956350226x_{10} = -23.8133956350226
x11=−85.7673275536261x_{11} = -85.7673275536261
x12=53.4535133009683x_{12} = 53.4535133009683
x13=0x_{13} = 0
x14=123.583369243266x_{14} = 123.583369243266
x15=63.0281077262879x_{15} = 63.0281077262879
x16=77.5334959297238x_{16} = 77.5334959297238
x17=18.1194601833497x_{17} = 18.1194601833497
x18=42.4836052898255x_{18} = 42.4836052898255
x19=−30.1059051977611x_{19} = -30.1059051977611
x20=−17.8563208080559x_{20} = -17.8563208080559
x21=6.26667578209062x_{21} = 6.26667578209062
x22=1.07180134799622x_{22} = 1.07180134799622
x23=41.9999210018193x_{23} = 41.9999210018193
x24=−53.6295256129204x_{24} = -53.6295256129204
x25=76.2258515383438x_{25} = 76.2258515383438
x26=−45.8958343802316x_{26} = -45.8958343802316
x27=−79.6717869621148x_{27} = -79.6717869621148
x28=−6.008807510337x_{28} = -6.008807510337
x29=−5.74727419627096x_{29} = -5.74727419627096
x30=28.0528972678513x_{30} = 28.0528972678513
x31=56.1199638171434x_{31} = 56.1199638171434
x32=−40.4375336170006x_{32} = -40.4375336170006
x33=1.07180134799621x_{33} = 1.07180134799621
x34=3.77031009470098x_{34} = 3.77031009470098
x35=−47.87258851768x_{35} = -47.87258851768
x36=36.0860637747281x_{36} = 36.0860637747281
x37=−77.8367347661307x_{37} = -77.8367347661307
x38=−7.83102368526207x_{38} = -7.83102368526207
x39=−31.9780665870872x_{39} = -31.9780665870872
x40=31.0306977554749x_{40} = 31.0306977554749
x41=54.1252365169635x_{41} = 54.1252365169635
x42=−4.53090580308408x_{42} = -4.53090580308408
x43=−35.6917795239445x_{43} = -35.6917795239445
x44=80.1827636412082x_{44} = 80.1827636412082
x45=−1.07180134799621x_{45} = -1.07180134799621
x46=−81.8117494870919x_{46} = -81.8117494870919
x47=32.1248043487951x_{47} = 32.1248043487951
x48=92.1079558673844x_{48} = 92.1079558673844
x49=−21.744058273147x_{49} = -21.744058273147
x50=20.2473087856324x_{50} = 20.2473087856324
x51=−97.8789272264631x_{51} = -97.8789272264631
x52=34.2087454964102x_{52} = 34.2087454964102
x53=10.2570609435673x_{53} = 10.2570609435673
x54=22.3147834698915x_{54} = 22.3147834698915
x55=−77.6144900088749x_{55} = -77.6144900088749
x56=4.144499701712x_{56} = 4.144499701712
x57=−93.7978280387191x_{57} = -93.7978280387191
x58=−65.8556585728539x_{58} = -65.8556585728539
x59=−47.8069247537141x_{59} = -47.8069247537141
x60=−3.77031009470098x_{60} = -3.77031009470098
x61=2.21234304383249x_{61} = 2.21234304383249
x62=84.3080687600362x_{62} = 84.3080687600362
x63=58.1813944632285x_{63} = 58.1813944632285
x64=−62.8784063450366x_{64} = -62.8784063450366
x65=7.61942227709894x_{65} = 7.61942227709894
x66=−75.7711223256984x_{66} = -75.7711223256984
x67=−90.2299374902237x_{67} = -90.2299374902237
x68=−33.7931822913434x_{68} = -33.7931822913434
x69=−45.9642370531503x_{69} = -45.9642370531503
x70=28.1646978075122x_{70} = 28.1646978075122
x71=94.2155500525576x_{71} = 94.2155500525576
x72=62.2255375583191x_{72} = 62.2255375583191
x73=−16.000961718966x_{73} = -16.000961718966
x74=−71.61456434202x_{74} = -71.61456434202
x75=40.1648554721824x_{75} = 40.1648554721824
x76=−97.7504590719906x_{76} = -97.7504590719906
Signos de extremos en los puntos:
(70.15196901176319, 1.50884608091918)

(-5.45689420149144, -0.320119040910535)

(98.43905193109056, 0.502141413380089)

(60.250360184395696, -1.84719239330664)

(16.00096171896595, -1.95734142734859)

(-9.295200303320142, -1.99159239923997)

(-19.2131827846554, -0.0653441436752971)

(-68.24526875729316, 1.64498694165504)

(90.2124794543957, 0.373463955522474)

(-23.813395635022637, 1.24860252790097)

(-85.76732755362612, -1.58627794456955)

(53.45351330096833, -1.99892184674017)

(0, 1)

(123.58336924326606, -1.48776999626358)

(63.028107726287885, 1.98080259093646)

(77.53349592972378, -1.53495826506863)

(18.1194601833497, 1.74494118614731)

(42.483605289825455, 1.07197310293439)

(-30.105905197761075, 1.25770066208084)

(-17.856320808055948, -0.453742435610938)

(6.2666757820906245, 1.99986285339417)

(1.0718013479962192, 1.39079925561018)

(41.999921001819274, -1.39999819474236)

(-53.629525612920446, -1.97535763224338)

(76.22585153834383, -0.32336399397888)

(-45.8958343802316, 0.663877523219909)

(-79.6717869621148, 0.575107136506196)

(-6.008807510337004, -0.0371518399924072)

(-5.747274196270963, 1.85881655289124)

(28.052897267851268, 0.0244094074002162)

(56.11996381714341, 1.90949841419268)

(-40.43753361700063, 0.0801666661315266)

(1.0718013479962063, 1.39079925561018)

(3.7703100947009753, 0.188171529732733)

(-47.87258851768004, -1.73254998445829)

(36.0860637747281, 0.957665004259692)

(-77.83673476613066, 0.237138019972482)

(-7.8310236852620685, -0.97500473999545)

(-31.978066587087238, -0.153848867127473)

(31.030697755474943, 1.92669415719388)

(54.125236516963454, 0.246964727214996)

(-4.530905803084081, 0.813603394896721)

(-35.69177952394449, -1.42272226306776)

(80.18276364120818, 1.07206904934775)

(-1.0718013479962063, 1.39079925561018)

(-81.8117494870919, 1.99151738113696)

(32.124804348795124, 1.75904154691855)

(92.10795586738436, 0.46117657150365)

(-21.74405827314698, 0.03035599441004)

(20.247308785632367, 1.17188523451614)

(-97.8789272264631, -1.8825393310492)

(34.2087454964102, 0.0601950205241431)

(10.257060943567257, -1.6725394180635)

(22.314783469891452, 0.0518888788102883)

(-77.61449000887494, -1.60156070469618)

(4.144499701711996, -1.53266836501194)

(-93.7978280387191, 1.90046547962862)

(-65.85565857285391, 0.00692849222149217)

(-47.806924753714064, -1.77563899825343)

(-3.7703100947009753, 0.188171529732733)

(2.2123430438324894, -1.58190583537133)

(84.30806876003615, 0.129669958874587)

(58.18139446322855, -1.0618540057132)

(-62.87840634503662, 1.99891652359167)

(7.619422277098935, 1.23037554740468)

(-75.77112232569843, -0.0687218727206863)

(-90.22993749022372, -1.64002827614011)

(-33.79318229134336, -1.72178899512071)

(-45.964237053150306, 0.600292418836843)

(28.164697807512244, 0.00600213023250085)

(94.21555005255756, -0.000519312533249106)

(62.22553755831907, 1.82174268895309)

(-16.00096171896595, -1.95734142734859)

(-71.61456434202, 0.199131431632696)

(40.16485547218239, -1.7801457943983)

(-97.75045907199062, -1.93551178280402)


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=−5.45689420149144x_{1} = -5.45689420149144
x2=60.2503601843957x_{2} = 60.2503601843957
x3=16.000961718966x_{3} = 16.000961718966
x4=−9.29520030332014x_{4} = -9.29520030332014
x5=−19.2131827846554x_{5} = -19.2131827846554
x6=−85.7673275536261x_{6} = -85.7673275536261
x7=53.4535133009683x_{7} = 53.4535133009683
x8=0x_{8} = 0
x9=123.583369243266x_{9} = 123.583369243266
x10=77.5334959297238x_{10} = 77.5334959297238
x11=−17.8563208080559x_{11} = -17.8563208080559
x12=41.9999210018193x_{12} = 41.9999210018193
x13=−53.6295256129204x_{13} = -53.6295256129204
x14=76.2258515383438x_{14} = 76.2258515383438
x15=−6.008807510337x_{15} = -6.008807510337
x16=−47.87258851768x_{16} = -47.87258851768
x17=−7.83102368526207x_{17} = -7.83102368526207
x18=−31.9780665870872x_{18} = -31.9780665870872
x19=−35.6917795239445x_{19} = -35.6917795239445
x20=−97.8789272264631x_{20} = -97.8789272264631
x21=10.2570609435673x_{21} = 10.2570609435673
x22=−77.6144900088749x_{22} = -77.6144900088749
x23=4.144499701712x_{23} = 4.144499701712
x24=−47.8069247537141x_{24} = -47.8069247537141
x25=2.21234304383249x_{25} = 2.21234304383249
x26=58.1813944632285x_{26} = 58.1813944632285
x27=−75.7711223256984x_{27} = -75.7711223256984
x28=−90.2299374902237x_{28} = -90.2299374902237
x29=−33.7931822913434x_{29} = -33.7931822913434
x30=94.2155500525576x_{30} = 94.2155500525576
x31=−16.000961718966x_{31} = -16.000961718966
x32=40.1648554721824x_{32} = 40.1648554721824
x33=−97.7504590719906x_{33} = -97.7504590719906
Puntos máximos de la función:
x33=70.1519690117632x_{33} = 70.1519690117632
x33=98.4390519310906x_{33} = 98.4390519310906
x33=−68.2452687572932x_{33} = -68.2452687572932
x33=90.2124794543957x_{33} = 90.2124794543957
x33=−23.8133956350226x_{33} = -23.8133956350226
x33=63.0281077262879x_{33} = 63.0281077262879
x33=18.1194601833497x_{33} = 18.1194601833497
x33=42.4836052898255x_{33} = 42.4836052898255
x33=−30.1059051977611x_{33} = -30.1059051977611
x33=6.26667578209062x_{33} = 6.26667578209062
x33=1.07180134799622x_{33} = 1.07180134799622
x33=−45.8958343802316x_{33} = -45.8958343802316
x33=−79.6717869621148x_{33} = -79.6717869621148
x33=−5.74727419627096x_{33} = -5.74727419627096
x33=28.0528972678513x_{33} = 28.0528972678513
x33=56.1199638171434x_{33} = 56.1199638171434
x33=−40.4375336170006x_{33} = -40.4375336170006
x33=1.07180134799621x_{33} = 1.07180134799621
x33=3.77031009470098x_{33} = 3.77031009470098
x33=36.0860637747281x_{33} = 36.0860637747281
x33=−77.8367347661307x_{33} = -77.8367347661307
x33=31.0306977554749x_{33} = 31.0306977554749
x33=54.1252365169635x_{33} = 54.1252365169635
x33=−4.53090580308408x_{33} = -4.53090580308408
x33=80.1827636412082x_{33} = 80.1827636412082
x33=−1.07180134799621x_{33} = -1.07180134799621
x33=−81.8117494870919x_{33} = -81.8117494870919
x33=32.1248043487951x_{33} = 32.1248043487951
x33=92.1079558673844x_{33} = 92.1079558673844
x33=−21.744058273147x_{33} = -21.744058273147
x33=20.2473087856324x_{33} = 20.2473087856324
x33=34.2087454964102x_{33} = 34.2087454964102
x33=22.3147834698915x_{33} = 22.3147834698915
x33=−93.7978280387191x_{33} = -93.7978280387191
x33=−65.8556585728539x_{33} = -65.8556585728539
x33=−3.77031009470098x_{33} = -3.77031009470098
x33=84.3080687600362x_{33} = 84.3080687600362
x33=−62.8784063450366x_{33} = -62.8784063450366
x33=7.61942227709894x_{33} = 7.61942227709894
x33=−45.9642370531503x_{33} = -45.9642370531503
x33=28.1646978075122x_{33} = 28.1646978075122
x33=62.2255375583191x_{33} = 62.2255375583191
x33=−71.61456434202x_{33} = -71.61456434202
Decrece en los intervalos
[123.583369243266,∞)\left[123.583369243266, \infty\right)
Crece en los intervalos
(−∞,−97.8789272264631]\left(-\infty, -97.8789272264631\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
−4x2sin⁡(x2)−cos⁡(x)+2cos⁡(x2)=0- 4 x^{2} \sin{\left(x^{2} \right)} - \cos{\left(x \right)} + 2 \cos{\left(x^{2} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=32.5379363049001x_{1} = 32.5379363049001
x2=−3.96597452639216x_{2} = -3.96597452639216
x3=56.4687238951578x_{3} = 56.4687238951578
x4=3.96597452639216x_{4} = 3.96597452639216
x5=−1.80975781234634x_{5} = -1.80975781234634
x6=29.8699324919706x_{6} = 29.8699324919706
x7=22.1379759418508x_{7} = 22.1379759418508
x8=64.2499249705881x_{8} = 64.2499249705881
x9=−17.3664757501727x_{9} = -17.3664757501727
x10=96.1709355031846x_{10} = 96.1709355031846
x11=16.2448912466442x_{11} = 16.2448912466442
x12=98.1433805548582x_{12} = 98.1433805548582
x13=−5.88035955787882x_{13} = -5.88035955787882
x14=32.586173386629x_{14} = 32.586173386629
x15=2.52846300108139x_{15} = 2.52846300108139
x16=−7.30882080511085x_{16} = -7.30882080511085
x17=47.6918587778135x_{17} = 47.6918587778135
x18=6.14050561821415x_{18} = 6.14050561821415
x19=6.86577925072113x_{19} = 6.86577925072113
x20=−19.8166777316811x_{20} = -19.8166777316811
x21=−39.7914952202531x_{21} = -39.7914952202531
x22=−55.8533949445166x_{22} = -55.8533949445166
x23=−14.3995777476015x_{23} = -14.3995777476015
x24=24.1730602893892x_{24} = 24.1730602893892
x25=−6.63236935665398x_{25} = -6.63236935665398
x26=86.2148959962608x_{26} = 86.2148959962608
x27=−41.8314154133013x_{27} = -41.8314154133013
x28=18.2485534648576x_{28} = 18.2485534648576
x29=16.6271618289191x_{29} = 16.6271618289191
x30=−59.8449315621084x_{30} = -59.8449315621084
x31=8.12280846096423x_{31} = 8.12280846096423
x32=−70.8981548116471x_{32} = -70.8981548116471
x33=42.316759150157x_{33} = 42.316759150157
x34=−0.713144790484138x_{34} = -0.713144790484138
x35=83.925269272506x_{35} = 83.925269272506
x36=52.2498245194862x_{36} = 52.2498245194862
x37=46.2878655949837x_{37} = 46.2878655949837
x38=54.9174755267934x_{38} = 54.9174755267934
x39=−9.86874804833616x_{39} = -9.86874804833616
x40=−22.0668841520616x_{40} = -22.0668841520616
x41=−74.0198464629136x_{41} = -74.0198464629136
x42=−9.70853390286448x_{42} = -9.70853390286448
x43=7.09027424566051x_{43} = 7.09027424566051
x44=38.8729528235485x_{44} = 38.8729528235485
x45=−77.7660974414159x_{45} = -77.7660974414159
x46=−7.72652365795357x_{46} = -7.72652365795357
x47=36.8823821408824x_{47} = 36.8823821408824
x48=−95.8600989204202x_{48} = -95.8600989204202
x49=58.6786650501486x_{49} = 58.6786650501486
x50=−15.7539464263141x_{50} = -15.7539464263141
x51=9.86874804833616x_{51} = 9.86874804833616
x52=46.117875044883x_{52} = 46.117875044883
x53=−3.55304013017456x_{53} = -3.55304013017456
x54=86.7235427574972x_{54} = 86.7235427574972
x55=−100.280796556208x_{55} = -100.280796556208
x56=1.80975781234634x_{56} = 1.80975781234634
x57=78.2292950868904x_{57} = 78.2292950868904
x58=−11.2101410026769x_{58} = -11.2101410026769
x59=−87.3192158807728x_{59} = -87.3192158807728
x60=31.9533771682604x_{60} = 31.9533771682604
x61=94.1238084203925x_{61} = 94.1238084203925
x62=−89.7498948884268x_{62} = -89.7498948884268
x63=95.6304150068739x_{63} = 95.6304150068739
x64=−26.5868218408701x_{64} = -26.5868218408701
x65=−53.8779348241314x_{65} = -53.8779348241314
x66=73.4446367109013x_{66} = 73.4446367109013
x67=73.9349126178445x_{67} = 73.9349126178445
x68=−81.6483903603687x_{68} = -81.6483903603687
x69=80.2316859449595x_{69} = 80.2316859449595
x70=−16.4371380980319x_{70} = -16.4371380980319
x71=82.1853043240165x_{71} = 82.1853043240165
x72=−25.9287738130961x_{72} = -25.9287738130961
x73=48.5082785752935x_{73} = 48.5082785752935
x74=−2.52846300108139x_{74} = -2.52846300108139
x75=−67.5628169647967x_{75} = -67.5628169647967
x76=7.72652365795357x_{76} = 7.72652365795357
x77=3.07429241192371x_{77} = 3.07429241192371
x78=−33.86268724018x_{78} = -33.86268724018
x79=−63.8575551926871x_{79} = -63.8575551926871
x80=−9.21010404307196x_{80} = -9.21010404307196
x81=−60.9115837553156x_{81} = -60.9115837553156
x82=−43.8480881589469x_{82} = -43.8480881589469
x83=28.2482826698483x_{83} = 28.2482826698483

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
[95.6304150068739,∞)\left[95.6304150068739, \infty\right)
Convexa en los intervalos
(−∞,−89.7498948884268]\left(-\infty, -89.7498948884268\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(π−x2)+cos⁡(x))=⟨−2,2⟩\lim_{x \to -\infty}\left(\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−2,2⟩y = \left\langle -2, 2\right\rangle
lim⁡x→∞(sin⁡(π−x2)+cos⁡(x))=⟨−2,2⟩\lim_{x \to \infty}\left(\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−2,2⟩y = \left\langle -2, 2\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(pi - x^2) + cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(π−x2)+cos⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(π−x2)+cos⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
sin⁡(π−x2)+cos⁡(x)=sin⁡(π−x2)+cos⁡(x)\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)} = \sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)}
- Sí
sin⁡(π−x2)+cos⁡(x)=−sin⁡(π−x2)−cos⁡(x)\sin{\left(\pi - x^{2} \right)} + \cos{\left(x \right)} = - \sin{\left(\pi - x^{2} \right)} - \cos{\left(x \right)}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор