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Trazado el gráfico de la función/ cos(x^2+(143/100)*pi)+x/2

Gráfico de la función y = cos(x^2+(143/100)*pi)+x/2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          / 2   143*pi\   x
f(x) = cos|x  + ------| + -
          \      100  /   2
f(x)=x2+cos⁡(x2+143π100)f{\left(x \right)} = \frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)} 
f = x/2 + cos(x^2 + 143*pi/100)
Gráfico de la función
02468-8-6-4-2-1010-1010
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:
x2+cos⁡(x2+143π100)=0\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=0.280985079359985x_{1} = 0.280985079359985
x2=−0.791811518047749x_{2} = -0.791811518047749
x3=−1.56845574157809x_{3} = -1.56845574157809
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 cos(x^2 + 143*pi/100) + x/2.
cos⁡(02+143π100)+02\cos{\left(0^{2} + \frac{143 \pi}{100} \right)} + \frac{0}{2}
Resultado:
f(0)=−cos⁡(43π100)f{\left(0 \right)} = - \cos{\left(\frac{43 \pi}{100} \right)}
Punto:
(0, -cos(43*pi/100))
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
2xsin⁡(x2+43π100)+12=02 x \sin{\left(x^{2} + \frac{43 \pi}{100} \right)} + \frac{1}{2} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−59.0673710336714x_{1} = -59.0673710336714
x2=−14.6765790799688x_{2} = -14.6765790799688
x3=18.1254003272219x_{3} = 18.1254003272219
x4=−0.253067907308303x_{4} = -0.253067907308303
x5=−7.84301275894851x_{5} = -7.84301275894851
x6=30.1094286758943x_{6} = 30.1094286758943
x7=−5.18413022918244x_{7} = -5.18413022918244
x8=82.1962161813902x_{8} = 82.1962161813902
x9=56.1219297718006x_{9} = 56.1219297718006
x10=−23.7517645351511x_{10} = -23.7517645351511
x11=−45.898282526298x_{11} = -45.898282526298
x12=−3.78033045426059x_{12} = -3.78033045426059
x13=28.0006848145669x_{13} = 28.0006848145669
x14=−1.26142724762611x_{14} = -1.26142724762611
x15=−79.8110402703968x_{15} = -79.8110402703968
x16=−85.7503037998523x_{16} = -85.7503037998523
x17=22.2488093531615x_{17} = 22.2488093531615
x18=57.9397616208939x_{18} = 57.9397616208939
x19=−69.771923517515x_{19} = -69.771923517515
x20=39.6559369940426x_{20} = 39.6559369940426
x21=−71.813283824168x_{21} = -71.813283824168
x22=−91.7503141769514x_{22} = -91.7503141769514
x23=6.76830482747729x_{23} = 6.76830482747729
x24=10.2683453538832x_{24} = 10.2683453538832
x25=−54.3010130006599x_{25} = -54.3010130006599
x26=−83.7298447614051x_{26} = -83.7298447614051
x27=92.0920548428205x_{27} = 92.0920548428205
x28=19.5425337645512x_{28} = 19.5425337645512
x29=−118.563376012134x_{29} = -118.563376012134
x30=−37.706550585261x_{30} = -37.706550585261
x31=−16.105458146094x_{31} = -16.105458146094
x32=9.63695751046927x_{32} = 9.63695751046927
x33=−93.0929673010935x_{33} = -93.0929673010935
x34=−12.8504501866847x_{34} = -12.8504501866847
x35=44.189524643429x_{35} = 44.189524643429
x36=−5.75875060292414x_{36} = -5.75875060292414
x37=96.0168014316188x_{37} = 96.0168014316188
x38=−21.7489795348122x_{38} = -21.7489795348122
x39=98.1684920416309x_{39} = 98.1684920416309
x40=4.17597521630883x_{40} = 4.17597521630883
x41=−6.99645178806103x_{41} = -6.99645178806103
x42=20.2536440313951x_{42} = 20.2536440313951
x43=32.1285057156498x_{43} = 32.1285057156498
x44=51.8444558703893x_{44} = 51.8444558703893
x45=−42.1146414946693x_{45} = -42.1146414946693
x46=40.1674185766779x_{46} = 40.1674185766779
x47=−81.4475037616697x_{47} = -81.4475037616697
x48=−33.7496643074153x_{48} = -33.7496643074153
x49=84.1602252820932x_{49} = 84.1602252820932
x50=−65.8812109568259x_{50} = -65.8812109568259
x51=2.19503055863999x_{51} = 2.19503055863999
x52=54.4454588407555x_{52} = 54.4454588407555
x53=34.120189283569x_{53} = 34.120189283569
x54=−0.253067907308303x_{54} = -0.253067907308303
x55=14.2432507074974x_{55} = 14.2432507074974
x56=94.2667353005108x_{56} = 94.2667353005108
x57=−97.6390304045964x_{57} = -97.6390304045964
x58=−77.9793286614609x_{58} = -77.9793286614609
x59=26.5020081536426x_{59} = 26.5020081536426
x60=−55.7568859063973x_{60} = -55.7568859063973
x61=−35.9142970794647x_{61} = -35.9142970794647
x62=−47.8750140912127x_{62} = -47.8750140912127
x63=41.8903971872546x_{63} = 41.8903971872546
x64=6.02550618610396x_{64} = 6.02550618610396
x65=1.40349228286476x_{65} = 1.40349228286476
x66=−14.2420182224566x_{66} = -14.2420182224566
x67=3.33774094289165x_{67} = 3.33774094289165
x68=−43.2191041037829x_{68} = -43.2191041037829
x69=39.0170214092997x_{69} = 39.0170214092997
x70=−95.1127677336722x_{70} = -95.1127677336722
x71=8.42231759038549x_{71} = 8.42231759038549
x72=65.761888664752x_{72} = 65.761888664752
x73=13.3318659450388x_{73} = 13.3318659450388
x74=12.7276191630586x_{74} = 12.7276191630586
x75=90.2311171525508x_{75} = 90.2311171525508
x76=61.4908334991748x_{76} = 61.4908334991748
x77=80.1057178191658x_{77} = 80.1057178191658
x78=60.3043055043592x_{78} = 60.3043055043592
x79=−63.6498826867489x_{79} = -63.6498826867489
x80=−57.7496739585048x_{80} = -57.7496739585048
x81=40.942074763623x_{81} = 40.942074763623
x82=−17.863526003547x_{82} = -17.863526003547
x83=77.534858159205x_{83} = 77.534858159205
Signos de extremos en los puntos:
                                            /                   43*pi\ 
(-59.06737103367145, -29.5336855168357 - cos|3488.95432082941 + -----|)
                                            \                    100 / 

                                             /                   43*pi\ 
(-14.676579079968846, -7.33828953998442 - cos|215.401973490579 + -----|)
                                             \                    100 / 

                                           /                   43*pi\ 
(18.125400327221886, 9.06270016361094 - cos|328.530137022055 + -----|)
                                           \                    100 / 

                                               /                     43*pi\ 
(-0.25306790730830264, -0.126533953654151 - cos|0.0640433657094037 + -----|)
                                               \                      100 / 

                                            /                   43*pi\ 
(-7.843012758948514, -3.92150637947426 - cos|61.5128491370292 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(30.10942867589428, 15.0547143379471 - cos|906.577695188765 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-5.184130229182436, -2.59206511459122 - cos|26.8752062331231 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(82.19621618139017, 41.0981080906951 - cos|6756.21795453783 + -----|)
                                          \                    100 / 

                                          /                   43*pi\ 
(56.12192977180059, 28.0609648859003 - cos|3149.67100131092 + -----|)
                                          \                    100 / 

                                             /                  43*pi\ 
(-23.751764535151057, -11.8758822675755 - cos|564.14631853326 + -----|)
                                             \                   100 / 

                                           /                   43*pi\ 
(-45.89828252629801, -22.949141263149 - cos|2106.65233886387 + -----|)
                                           \                    100 / 

                                            /                   43*pi\ 
(-3.7803304542605902, -1.8901652271303 - cos|14.2908983434101 + -----|)
                                            \                    100 / 

                                           /                   43*pi\ 
(28.000684814566895, 14.0003424072834 - cos|784.038350084717 + -----|)
                                           \                    100 / 

                                              /                   43*pi\ 
(-1.2614272476261092, -0.630713623813055 - cos|1.59119870105358 + -----|)
                                              \                    100 / 

                                            /                  43*pi\ 
(-79.81104027039677, -39.9055201351984 - cos|6369.8021490429 + -----|)
                                            \                   100 / 

                                            /                   43*pi\ 
(-85.75030379985232, -42.8751518999262 - cos|7353.11460176697 + -----|)
                                            \                    100 / 

                                           /                   43*pi\ 
(22.248809353161487, 11.1244046765807 - cos|495.009517633326 + -----|)
                                           \                    100 / 

                                          /                   43*pi\ 
(57.93976162089389, 28.9698808104469 - cos|3357.01597668601 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-69.77192351751503, -34.8859617587575 - cos|4868.12131133397 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(39.65593699404262, 19.8279684970213 - cos|1572.59333887548 + -----|)
                                          \                    100 / 

                                           /                   43*pi\ 
(-71.81328382416798, -35.906641912084 - cos|5157.14773361051 + -----|)
                                           \                    100 / 

                                            /                   43*pi\ 
(-91.75031417695138, -45.8751570884757 - cos|8418.12015156928 + -----|)
                                            \                    100 / 

                                         /                   43*pi\ 
(6.76830482747729, 3.38415241373864 - cos|45.8099502376524 + -----|)
                                         \                    100 / 

                                           /                   43*pi\ 
(10.268345353883186, 5.13417267694159 - cos|105.438916306614 + -----|)
                                           \                    100 / 

                                             /                   43*pi\ 
(-54.301013000659864, -27.1505065003299 - cos|2948.60001289783 + -----|)
                                             \                    100 / 

                                           /                 43*pi\ 
(-83.7298447614051, -41.8649223807026 - cos|7010.686903769 + -----|)
                                           \                  100 / 

                                          /                   43*pi\ 
(92.09205484282047, 46.0460274214102 - cos|8480.94656517305 + -----|)
                                          \                    100 / 

                                         /                   43*pi\ 
(19.54253376455119, 9.7712668822756 - cos|381.910625938623 + -----|)
                                         \                    100 / 

                                             /                   43*pi\ 
(-118.56337601213447, -59.2816880060672 - cos|14057.2741313948 + -----|)
                                             \                    100 / 

                                          /                   43*pi\ 
(-37.706550585261, -18.8532752926305 - cos|1421.78395703885 + -----|)
                                          \                    100 / 

                                             /                   43*pi\ 
(-16.105458146093962, -8.05272907304698 - cos|259.385782095584 + -----|)
                                             \                    100 / 

                                          /                 43*pi\ 
(9.636957510469266, 4.81847875523463 - cos|92.87095005859 + -----|)
                                          \                  100 / 

                                            /                   43*pi\ 
(-93.09296730109352, -46.5464836505468 - cos|8666.30056092247 + -----|)
                                            \                    100 / 

                                             /                   43*pi\ 
(-12.850450186684657, -6.42522509334233 - cos|165.134070000464 + -----|)
                                             \                    100 / 

                                          /                   43*pi\ 
(44.18952464342902, 22.0947623217145 - cos|1952.71408821222 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-5.758750602924143, -2.87937530146207 - cos|33.1632085066792 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(96.01680143161883, 48.0084007158094 - cos|9219.22615715892 + -----|)
                                          \                    100 / 

                                             /                  43*pi\ 
(-21.748979534812193, -10.8744897674061 - cos|473.01811080568 + -----|)
                                             \                   100 / 

                                          /                   43*pi\ 
(98.16849204163086, 49.0842460208154 - cos|9637.05282972774 + -----|)
                                          \                    100 / 

                                          /                   43*pi\ 
(4.175975216308828, 2.08798760815441 - cos|17.4387690072256 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-6.996451788061027, -3.49822589403051 - cos|48.9503376226623 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(20.25364403139506, 10.1268220156975 - cos|410.210096550465 + -----|)
                                          \                    100 / 

                                          /                   43*pi\ 
(32.12850571564983, 16.0642528578249 - cos|1032.24087952054 + -----|)
                                          \                    100 / 

                                           /                   43*pi\ 
(51.844455870389346, 25.9222279351947 - cos|2687.84760449675 + -----|)
                                           \                    100 / 

                                            /                   43*pi\ 
(-42.11464149466932, -21.0573207473347 - cos|1773.64302822452 + -----|)
                                            \                    100 / 

                                           /                   43*pi\ 
(40.167418576677875, 20.0837092883389 - cos|1613.42151511405 + -----|)
                                           \                    100 / 

                                            /                  43*pi\ 
(-81.44750376166971, -40.7237518808349 - cos|6633.6958690072 + -----|)
                                            \                   100 / 

                                             /                   43*pi\ 
(-33.749664307415294, -16.8748321537076 - cos|1139.03984086322 + -----|)
                                             \                    100 / 

                                          /                   43*pi\ 
(84.16022528209318, 42.0801126410466 - cos|7082.94351953268 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-65.88121095682585, -32.9406054784129 - cos|4340.33395713779 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(2.195030558639986, 1.09751527931999 - cos|4.81815915336337 + -----|)
                                          \                    100 / 

                                          /                  43*pi\ 
(54.44545884075552, 27.2227294203778 - cos|2964.3079883804 + -----|)
                                          \                   100 / 

                                          /                   43*pi\ 
(34.12018928356896, 17.0600946417845 - cos|1164.18731674657 + -----|)
                                          \                    100 / 

                                              /                     43*pi\ 
(-0.2530679073083027, -0.126533953654151 - cos|0.0640433657094037 + -----|)
                                              \                      100 / 

                                           /                   43*pi\ 
(14.243250707497385, 7.12162535374869 - cos|202.870190716625 + -----|)
                                           \                    100 / 

                                          /                   43*pi\ 
(94.26673530051085, 47.1333676502554 - cos|8886.21738421658 + -----|)
                                          \                    100 / 

                                           /                  43*pi\ 
(-97.6390304045964, -48.8195152022982 - cos|9533.3802583497 + -----|)
                                           \                   100 / 

                                            /                   43*pi\ 
(-77.97932866146087, -38.9896643307304 - cos|6080.77569849213 + -----|)
                                            \                    100 / 

                                           /                   43*pi\ 
(26.502008153642645, 13.2510040768213 - cos|702.356436175741 + -----|)
                                           \                    100 / 

                                             /                 43*pi\ 
(-55.756885906397265, -27.8784429531986 - cos|3108.830325979 + -----|)
                                             \                  100 / 

                                             /                   43*pi\ 
(-35.914297079464724, -17.9571485397324 - cos|1289.83673471205 + -----|)
                                             \                    100 / 

                                            /                   43*pi\ 
(-47.87501409121271, -23.9375070456064 - cos|2292.01697423382 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(41.89039718725462, 20.9451985936273 - cos|1754.80537650595 + -----|)
                                          \                    100 / 

                                         /                   43*pi\ 
(6.02550618610396, 3.01275309305198 - cos|36.3067247987771 + -----|)
                                         \                    100 / 

                                           /                   43*pi\ 
(1.403492282864759, 0.701746141432379 - cos|1.96979058806093 + -----|)
                                           \                    100 / 

                                            /                   43*pi\ 
(-14.242018222456595, -7.1210091112283 - cos|202.835083048786 + -----|)
                                            \                    100 / 

                                           /                   43*pi\ 
(3.3377409428916542, 1.66887047144583 - cos|11.1405146018553 + -----|)
                                           \                    100 / 

                                            /                   43*pi\ 
(-43.21910410378293, -21.6095520518915 - cos|1867.89095953363 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(39.01702140929966, 19.5085107046498 - cos|1522.32795965375 + -----|)
                                          \                    100 / 

                                            /                   43*pi\ 
(-95.11276773367221, -47.5563838668361 - cos|9046.43858595948 + -----|)
                                            \                    100 / 

                                          /                   43*pi\ 
(8.422317590385488, 4.21115879519274 - cos|70.9354335933168 + -----|)
                                          \                    100 / 

                                         /                   43*pi\ 
(65.76188866475201, 32.880944332376 - cos|4324.62600075524 + -----|)
                                         \                    100 / 

                                          /                   43*pi\ 
(13.33186594503883, 6.66593297251941 - cos|177.738649576486 + -----|)
                                          \                    100 / 

                                           /                   43*pi\ 
(12.727619163058622, 6.36380958152931 - cos|161.992289559857 + -----|)
                                           \                    100 / 

                                          /                   43*pi\ 
(90.23111715255082, 45.1155585762754 - cos|8141.65450259735 + -----|)
                                          \                    100 / 

                                          /                   43*pi\ 
(61.49083349917479, 30.7454167495874 - cos|3781.12260442324 + -----|)
                                          \                    100 / 

                                         /                   43*pi\ 
(80.1057178191658, 40.0528589095829 - cos|6416.92602732382 + -----|)
                                         \                    100 / 

                                          /                   43*pi\ 
(60.30430550435918, 30.1521527521796 - cos|3636.60926236308 + -----|)
                                          \                    100 / 

                                             /                  43*pi\ 
(-63.649882686748924, -31.8249413433745 - cos|4051.3075660369 + -----|)
                                             \                   100 / 

                                           /                   43*pi\ 
(-57.7496739585048, -28.8748369792524 - cos|3335.02484231361 + -----|)
                                           \                    100 / 

                                          /                  43*pi\ 
(40.94207476362302, 20.4710373818115 - cos|1676.2534859501 + -----|)
                                          \                   100 / 

                                             /                 43*pi\ 
(-17.863526003547012, -8.93176300177351 - cos|319.1055612794 + -----|)
                                             \                  100 / 

                                          /                   43*pi\ 
(77.53485815920503, 38.7674290796025 - cos|6011.65422976804 + -----|)
                                          \                    100 /


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=−0.253067907308303x_{1} = -0.253067907308303
x2=−7.84301275894851x_{2} = -7.84301275894851
x3=−23.7517645351511x_{3} = -23.7517645351511
x4=28.0006848145669x_{4} = 28.0006848145669
x5=−79.8110402703968x_{5} = -79.8110402703968
x6=22.2488093531615x_{6} = 22.2488093531615
x7=−69.771923517515x_{7} = -69.771923517515
x8=−71.813283824168x_{8} = -71.813283824168
x9=−91.7503141769514x_{9} = -91.7503141769514
x10=10.2683453538832x_{10} = 10.2683453538832
x11=−83.7298447614051x_{11} = -83.7298447614051
x12=92.0920548428205x_{12} = 92.0920548428205
x13=19.5425337645512x_{13} = 19.5425337645512
x14=9.63695751046927x_{14} = 9.63695751046927
x15=44.189524643429x_{15} = 44.189524643429
x16=98.1684920416309x_{16} = 98.1684920416309
x17=4.17597521630883x_{17} = 4.17597521630883
x18=−6.99645178806103x_{18} = -6.99645178806103
x19=51.8444558703893x_{19} = 51.8444558703893
x20=40.1674185766779x_{20} = 40.1674185766779
x21=−81.4475037616697x_{21} = -81.4475037616697
x22=−65.8812109568259x_{22} = -65.8812109568259
x23=2.19503055863999x_{23} = 2.19503055863999
x24=54.4454588407555x_{24} = 54.4454588407555
x25=−0.253067907308303x_{25} = -0.253067907308303
x26=−77.9793286614609x_{26} = -77.9793286614609
x27=26.5020081536426x_{27} = 26.5020081536426
x28=−55.7568859063973x_{28} = -55.7568859063973
x29=−47.8750140912127x_{29} = -47.8750140912127
x30=6.02550618610396x_{30} = 6.02550618610396
x31=3.33774094289165x_{31} = 3.33774094289165
x32=−95.1127677336722x_{32} = -95.1127677336722
x33=12.7276191630586x_{33} = 12.7276191630586
x34=90.2311171525508x_{34} = 90.2311171525508
x35=61.4908334991748x_{35} = 61.4908334991748
x36=60.3043055043592x_{36} = 60.3043055043592
x37=−63.6498826867489x_{37} = -63.6498826867489
x38=−57.7496739585048x_{38} = -57.7496739585048
x39=40.942074763623x_{39} = 40.942074763623
x40=−17.863526003547x_{40} = -17.863526003547
x41=77.534858159205x_{41} = 77.534858159205
Puntos máximos de la función:
x41=−59.0673710336714x_{41} = -59.0673710336714
x41=−14.6765790799688x_{41} = -14.6765790799688
x41=18.1254003272219x_{41} = 18.1254003272219
x41=30.1094286758943x_{41} = 30.1094286758943
x41=−5.18413022918244x_{41} = -5.18413022918244
x41=82.1962161813902x_{41} = 82.1962161813902
x41=56.1219297718006x_{41} = 56.1219297718006
x41=−45.898282526298x_{41} = -45.898282526298
x41=−3.78033045426059x_{41} = -3.78033045426059
x41=−1.26142724762611x_{41} = -1.26142724762611
x41=−85.7503037998523x_{41} = -85.7503037998523
x41=57.9397616208939x_{41} = 57.9397616208939
x41=39.6559369940426x_{41} = 39.6559369940426
x41=6.76830482747729x_{41} = 6.76830482747729
x41=−54.3010130006599x_{41} = -54.3010130006599
x41=−118.563376012134x_{41} = -118.563376012134
x41=−37.706550585261x_{41} = -37.706550585261
x41=−16.105458146094x_{41} = -16.105458146094
x41=−93.0929673010935x_{41} = -93.0929673010935
x41=−12.8504501866847x_{41} = -12.8504501866847
x41=−5.75875060292414x_{41} = -5.75875060292414
x41=96.0168014316188x_{41} = 96.0168014316188
x41=−21.7489795348122x_{41} = -21.7489795348122
x41=20.2536440313951x_{41} = 20.2536440313951
x41=32.1285057156498x_{41} = 32.1285057156498
x41=−42.1146414946693x_{41} = -42.1146414946693
x41=−33.7496643074153x_{41} = -33.7496643074153
x41=84.1602252820932x_{41} = 84.1602252820932
x41=34.120189283569x_{41} = 34.120189283569
x41=14.2432507074974x_{41} = 14.2432507074974
x41=94.2667353005108x_{41} = 94.2667353005108
x41=−97.6390304045964x_{41} = -97.6390304045964
x41=−35.9142970794647x_{41} = -35.9142970794647
x41=41.8903971872546x_{41} = 41.8903971872546
x41=1.40349228286476x_{41} = 1.40349228286476
x41=−14.2420182224566x_{41} = -14.2420182224566
x41=−43.2191041037829x_{41} = -43.2191041037829
x41=39.0170214092997x_{41} = 39.0170214092997
x41=8.42231759038549x_{41} = 8.42231759038549
x41=65.761888664752x_{41} = 65.761888664752
x41=13.3318659450388x_{41} = 13.3318659450388
x41=80.1057178191658x_{41} = 80.1057178191658
Decrece en los intervalos
[98.1684920416309,∞)\left[98.1684920416309, \infty\right)
Crece en los intervalos
(−∞,−95.1127677336722]\left(-\infty, -95.1127677336722\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x2+cos⁡(x2+143π100))=−∞\lim_{x \to -\infty}\left(\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}\right) = -\infty
Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda
lim⁡x→∞(x2+cos⁡(x2+143π100))=∞\lim_{x \to \infty}\left(\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}\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 cos(x^2 + 143*pi/100) + x/2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(x2+cos⁡(x2+143π100)x)=12\lim_{x \to -\infty}\left(\frac{\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}}{x}\right) = \frac{1}{2}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=x2y = \frac{x}{2}
lim⁡x→∞(x2+cos⁡(x2+143π100)x)=12\lim_{x \to \infty}\left(\frac{\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}}{x}\right) = \frac{1}{2}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=x2y = \frac{x}{2}
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:
x2+cos⁡(x2+143π100)=−x2+cos⁡(x2+143π100)\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)} = - \frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}
- No
x2+cos⁡(x2+143π100)=x2−cos⁡(x2+143π100)\frac{x}{2} + \cos{\left(x^{2} + \frac{143 \pi}{100} \right)} = \frac{x}{2} - \cos{\left(x^{2} + \frac{143 \pi}{100} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор