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Trazado el gráfico de la función/ cos(5*x)+1/x

Gráfico de la función y = cos(5*x)+1/x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                  1
f(x) = cos(5*x) + -
                  x
f(x)=cos⁡(5x)+1xf{\left(x \right)} = \cos{\left(5 x \right)} + \frac{1}{x} 
f = cos(5*x) + 1/x
Gráfico de la función
02468-8-6-4-2-1010-5050
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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:
cos⁡(5x)+1x=0\cos{\left(5 x \right)} + \frac{1}{x} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=46.1770805161843x_{1} = 46.1770805161843
x2=26.0675447659125x_{2} = 26.0675447659125
x3=66.28458758361x_{3} = 66.28458758361
x4=−4.03396912365148x_{4} = -4.03396912365148
x5=−60.0077527405267x_{5} = -60.0077527405267
x6=−26.0828887668621x_{6} = -26.0828887668621
x7=16.0096219082539x_{7} = 16.0096219082539
x8=48.0705284534533x_{8} = 48.0705284534533
x9=17.9182457347446x_{9} = 17.9182457347446
x10=56.2309515517382x_{10} = 56.2309515517382
x11=−28.5954886842466x_{11} = -28.5954886842466
x12=−69.4263167927281x_{12} = -69.4263167927281
x13=54.3532327486638x_{13} = 54.3532327486638
x14=−102.099802342697x_{14} = -102.099802342697
x15=21.0391611137067x_{15} = 21.0391611137067
x16=−76.9664214040531x_{16} = -76.9664214040531
x17=−31.7237803378442x_{17} = -31.7237803378442
x18=78.2282137663733x_{18} = 78.2282137663733
x19=−73.8301363631026x_{19} = -73.8301363631026
x20=−92.0464918924178x_{20} = -92.0464918924178
x21=71.9452517483104x_{21} = 71.9452517483104
x22=−29.8518312192704x_{22} = -29.8518312192704
x23=39.8932127912823x_{23} = 39.8932127912823
x24=24.1985307514528x_{24} = 24.1985307514528
x25=83.8781393828607x_{25} = 83.8781393828607
x26=−16.0346036571737x_{26} = -16.0346036571737
x27=−85.7631473861886x_{27} = -85.7631473861886
x28=72.5680341762712x_{28} = 72.5680341762712
x29=12.2358476837394x_{29} = 12.2358476837394
x30=−53.7249572560403x_{30} = -53.7249572560403
x31=44.3009713727869x_{31} = 44.3009713727869
x32=−19.8021379349148x_{32} = -19.8021379349148
x33=−97.7055785284095x_{33} = -97.7055785284095
x34=−6.00250156887858x_{34} = -6.00250156887858
x35=60.0010862562463x_{35} = 60.0010862562463
x36=−71.9396915712252x_{36} = -71.9396915712252
x37=5.93516708575799x_{37} = 5.93516708575799
x38=−51.8324199559248x_{38} = -51.8324199559248
x39=58.1229052454183x_{39} = 58.1229052454183
x40=93.93149109073x_{40} = 93.93149109073
x41=76.3380814829268x_{41} = 76.3380814829268
x42=−70.0603709528519x_{42} = -70.0603709528519
x43=70.0546611645591x_{43} = 70.0546611645591
x44=22.2963347462524x_{44} = 22.2963347462524
x45=32.3522213914458x_{45} = 32.3522213914458
x46=−63.7774669001666x_{46} = -63.7774669001666
x47=−27.9530182275029x_{47} = -27.9530182275029
x48=68.1754942935297x_{48} = 68.1754942935297
x49=81.9980074028176x_{49} = 81.9980074028176
x50=−65.6562401732929x_{50} = -65.6562401732929
x51=100.214809903383x_{51} = 100.214809903383
x52=−33.6209909354981x_{52} = -33.6209909354981
x53=−75.7097412067054x_{53} = -75.7097412067054
x54=−95.8164885731804x_{54} = -95.8164885731804
x55=−80.113109201701x_{55} = -80.113109201701
x56=2.09984330284713x_{56} = 2.09984330284713
x57=92.050837505362x_{57} = 92.050837505362
x58=−9.75946617994244x_{58} = -9.75946617994244
x59=38.0185323075562x_{59} = 38.0185323075562
x60=14.1513116953682x_{60} = 14.1513116953682
x61=31.0953343282952x_{61} = 31.0953343282952
x62=−11.6066399122437x_{62} = -11.6066399122437
x63=−7.82836351403752x_{63} = -7.82836351403752
x64=−54.3458725671178x_{64} = -54.3458725671178
x65=−87.6527168165546x_{65} = -87.6527168165546
x66=27.9673273433605x_{66} = 27.9673273433605
x67=49.9473187055694x_{67} = 49.9473187055694
x68=−61.8861433938547x_{68} = -61.8861433938547
x69=88.281019106975x_{69} = 88.281019106975
x70=7.87943280899965x_{70} = 7.87943280899965
x71=−17.8958965550393x_{71} = -17.8958965550393
x72=61.8926068200493x_{72} = 61.8926068200493
x73=−21.6677557246461x_{73} = -21.6677557246461
x74=−93.9357494974102x_{74} = -93.9357494974102
x75=90.1614908706098x_{75} = 90.1614908706098
x76=80.1081159757586x_{76} = 80.1081159757586
x77=−81.993128969438x_{77} = -81.993128969438
x78=−36.1338511990879x_{78} = -36.1338511990879
x79=36.1227781361376x_{79} = 36.1227781361376
x80=4.13294712956785x_{80} = 4.13294712956785
x81=−41.7783946721586x_{81} = -41.7783946721586
x82=−83.8829081832692x_{82} = -83.8829081832692
x83=10.386541318275x_{83} = 10.386541318275
x84=−43.6727178032279x_{84} = -43.6727178032279
x85=−39.9032393497805x_{85} = -39.9032393497805
x86=−49.9553270365417x_{86} = -49.9553270365417
x87=−48.062206025799x_{87} = -48.062206025799
x88=−58.1160225298259x_{88} = -58.1160225298259
x89=98.3338839793345x_{89} = 98.3338839793345
x90=−14.1229937778661x_{90} = -14.1229937778661
x91=−38.0080084522323x_{91} = -38.0080084522323
x92=34.2492003065638x_{92} = 34.2492003065638
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(5*x) + 1/x.
10+cos⁡(0⋅5)\frac{1}{0} + \cos{\left(0 \cdot 5 \right)}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
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
−5sin⁡(5x)−1x2=0- 5 \sin{\left(5 x \right)} - \frac{1}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−64.0884998719047x_{1} = -64.0884998719047
x2=76.0265491372449x_{2} = 76.0265491372449
x3=70.3716673631468x_{3} = 70.3716673631468
x4=5850.90215804446x_{4} = 5850.90215804446
x5=38.3274576033144x_{5} = 38.3274576033144
x6=52.1504527572588x_{6} = 52.1504527572588
x7=45.8672717555654x_{7} = 45.8672717555654
x8=96.1327395281477x_{8} = 96.1327395281477
x9=−71.6283202981817x_{9} = -71.6283202981817
x10=−13.8232170107815x_{10} = -13.8232170107815
x11=65.9734549155131x_{11} = 65.9734549155131
x12=6.28217176404258x_{12} = 6.28217176404258
x13=−59.6902491914779x_{13} = -59.6902491914779
x14=30.1592454981252x_{14} = 30.1592454981252
x15=42.0973641290712x_{15} = 42.0973641290712
x16=−76.0265352964986x_{16} = -76.0265352964986
x17=18.2213578662666x_{17} = 18.2213578662666
x18=40.2123612293018x_{18} = 40.2123612293018
x19=54.0353799422805x_{19} = 54.0353799422805
x20=−89.8495449378441x_{20} = -89.8495449378441
x21=−86.0796333100335x_{21} = -86.0796333100335
x22=−37.6991399878088x_{22} = -37.6991399878088
x23=−57.8053167968865x_{23} = -57.8053167968865
x24=−55.9203364424288x_{24} = -55.9203364424288
x25=26.3893208515907x_{25} = 26.3893208515907
x26=50.2654666259918x_{26} = 50.2654666259918
x27=−35.8141250655249x_{27} = -35.8141250655249
x28=86.0796441066858x_{28} = 86.0796441066858
x29=−1.87355407126933x_{29} = -1.87355407126933
x30=74.141579347988x_{30} = 74.141579347988
x31=82.3097334282055x_{31} = 82.3097334282055
x32=72.2566386939008x_{32} = 72.2566386939008
x33=−27.6460676867148x_{33} = -27.6460676867148
x34=16.3361319124947x_{34} = 16.3361319124947
x35=1.89608744677742x_{35} = 1.89608744677742
x36=67.8583926308789x_{36} = 67.8583926308789
x37=−49.6371476919406x_{37} = -49.6371476919406
x38=11.9383327386359x_{38} = 11.9383327386359
x39=20.1060940355284x_{39} = 20.1060940355284
x40=−65.9734365352531x_{40} = -65.9734365352531
x41=−52.7787709398789x_{41} = -52.7787709398789
x42=99.9026503919548x_{42} = 99.9026503919548
x43=−69.7433486862369x_{43} = -69.7433486862369
x44=−20.1062919284733x_{44} = -20.1062919284733
x45=−7.54052585811551x_{45} = -7.54052585811551
x46=−3.77272156255489x_{46} = -3.77272156255489
x47=21.9912312856791x_{47} = 21.9912312856791
x48=39.5840929633375x_{48} = 39.5840929633375
x49=−81.6814149886701x_{49} = -81.6814149886701
x50=−96.1327308715469x_{50} = -96.1327308715469
x51=48.3805439543555x_{51} = 48.3805439543555
x52=−23.8761743338961x_{52} = -23.8761743338961
x53=−74.1415939014473x_{53} = -74.1415939014473
x54=87.9645891310655x_{54} = 87.9645891310655
x55=−67.8584100041957x_{55} = -67.8584100041957
x56=8.16874034587409x_{56} = 8.16874034587409
x57=32.0442840212249x_{57} = 32.0442840212249
x58=43.982276472445x_{58} = 43.982276472445
x59=−98.0176949554292x_{59} = -98.0176949554292
x60=−42.0973189870869x_{60} = -42.0973189870869
x61=−99.9026423763554x_{61} = -99.9026423763554
x62=−80.424778116052x_{62} = -80.424778116052
x63=84.1946774734577x_{63} = 84.1946774734577
x64=98.0176866285732x_{64} = 98.0176866285732
x65=−25.7609994848026x_{65} = -25.7609994848026
x66=−33.9292354053324x_{66} = -33.9292354053324
x67=23.8760339998439x_{67} = 23.8760339998439
x68=−21.9910658633337x_{68} = -21.9910658633337
x69=−87.9645994699618x_{69} = -87.9645994699618
x70=5.024964087331x_{70} = 5.024964087331
x71=−15.7078011506911x_{71} = -15.7078011506911
x72=−54.0354073411945x_{72} = -54.0354073411945
x73=−79.7964471192538x_{73} = -79.7964471192538
x74=−43.9823178280303x_{74} = -43.9823178280303
x75=10.0527006741872x_{75} = 10.0527006741872
x76=77.9114912194587x_{76} = 77.9114912194587
x77=55.9203620253561x_{77} = 55.9203620253561
x78=33.9291659120648x_{78} = 33.9291659120648
x79=64.088480394553x_{79} = 64.088480394553
x80=11.3094208157978x_{80} = 11.3094208157978
x81=89.2212263370942x_{81} = 89.2212263370942
x82=−45.8672337292251x_{82} = -45.8672337292251
x83=−10.0534922464597x_{83} = -10.0534922464597
x84=−93.6194565131637x_{84} = -93.6194565131637
x85=−11.937771402252x_{85} = -11.937771402252
x86=28.274383917284x_{86} = 28.274383917284
x87=92.3628287043813x_{87} = 92.3628287043813
x88=62.2035448789159x_{88} = 62.2035448789159
x89=−91.734510238114x_{89} = -91.734510238114
x90=94.2477751045297x_{90} = 94.2477751045297
x91=−32.0442061118175x_{91} = -32.0442061118175
x92=−77.9115043985929x_{92} = -77.9115043985929
x93=−47.7522258763082x_{93} = -47.7522258763082
x94=60.318567954868x_{94} = 60.318567954868
x95=−5.65361533565394x_{95} = -5.65361533565394
Signos de extremos en los puntos:
(-64.08849987190469, 0.984396575392199)

(76.02654913724491, -0.98684669951667)

(70.37166736314678, 1.01421026359159)

(5850.902158044462, 1.00017091381346)

(38.32745760331442, -0.973909034990737)

(52.15045275725882, -0.980824708355524)

(45.86727175556538, -0.978197957519864)

(96.13273952814767, -0.989597716371962)

(-71.62832029818166, 0.986039040839444)

(-13.823217010781464, 0.927657391829786)

(65.97345491551313, -0.984842387427931)

(6.282171764042585, 1.15916777973787)

(-59.690249191477896, -1.0167531534799)

(30.159245498125237, 1.03315730398472)

(42.097364129071195, -0.976245537249921)

(-76.02653529649857, -1.01315330168062)

(18.22135786626664, -0.945119166572271)

(40.212361229301756, 1.02486796750687)

(54.03537994228053, 1.01850639107756)

(-89.84954493784414, -1.01112971660701)

(-86.0796333100335, -1.01161714949507)

(-37.69913998780882, 0.973474186052939)

(-57.80531679688652, 0.982700551455186)

(-55.9203364424288, -1.01788257992076)

(26.389320851590714, 1.03789407530918)

(50.265466625991756, 1.01989437101942)

(-35.814125065524905, -1.02792193199728)

(86.07964410668582, -0.988382851233479)

(-1.873554071269333, -1.5321204436805)

(74.14157934798804, 1.01348770770357)

(82.30973342820555, -0.987850768138647)

(72.25663869390075, -0.986160440464841)

(-27.646067686714762, 0.963828456261764)

(16.336131912494725, 1.06121372046884)

(1.8960874467774207, -0.471049586846389)

(67.8583926308789, 1.01473656974803)

(-49.63714769194065, -1.02014619862269)

(11.938332738635912, -0.916235225114085)

(20.106094035528354, 1.04973604209747)

(-65.97343653525306, -1.01515761468353)

(-52.7787709398789, 0.981052985542718)

(99.90265039195478, -0.989990255352234)

(-69.74334868623691, -1.01433828400675)

(-20.10629192847326, 0.950264202662626)

(-7.540525858115513, 0.867377068110462)

(-3.772721562554892, 0.734840631657218)

(21.991231285679067, -0.95452724463018)

(39.584092963337525, -0.974737318766397)

(-81.68141498867006, 0.987757312519155)

(-96.1327308715469, -1.01040228409639)

(48.38054395435554, -0.97933053052164)

(-23.87617433389614, 0.958117181781256)

(-74.14159390144734, 0.986512293620199)

(87.96458913106545, 1.01136821055489)

(-67.85841000419572, 0.98526343213842)

(8.168740345874088, -0.877577613049669)

(32.04428402122487, -0.968793167381669)

(43.982276472445044, 1.02273642578634)

(-98.01769495542919, 0.989797760274888)

(-42.09731898708686, -1.02375447548632)

(-99.90264237635543, -1.01000974504933)

(-80.42477811605204, 0.987566020548993)

(84.19467747345767, 1.0118772349571)

(98.0176866285732, 1.01020224015846)

(-25.760999484802568, -1.03881832421558)

(-33.9292354053324, 0.970526877481966)

(23.876033999843887, 1.04188294130403)

(-21.991065863333695, -1.04547292639826)

(-87.96459946996175, 0.98863179011319)

(5.024964087331004, 1.19897502807381)

(-15.707801150691074, -1.06366230575499)

(-54.035407341194464, 0.981493613614322)

(-79.79644711925381, -1.01253188577611)

(-43.98231782803028, 0.977263584902935)

(10.052700674187209, 1.09947379766799)

(77.91149121945867, 1.01283507659858)

(55.920362025356134, -0.982117424169775)

(33.9291659120648, 1.02947315270125)

(64.08848039455296, 1.01560342697885)

(11.309420815797822, 1.08842063531684)

(89.2212263370942, 1.01120809489955)

(-45.867233729225056, -1.02180205151765)

(-10.053492246459658, 0.900530118494767)

(-93.61945651316368, -1.01068154006518)

(-11.93777140225203, -1.08376674425079)

(28.27438391728399, -0.964632266162313)

(92.3628287043813, -0.989173133397816)

(62.203544878915885, -0.983923744457917)

(-91.734510238114, 0.989098976782977)

(94.24777510452965, 1.01061032979294)

(-32.044206111817495, -1.03120687055505)

(-77.91150439859285, 0.987164924486982)

(-47.75222587630816, 0.9790585639659)

(60.31856795486797, 1.01657864141627)

(-5.653615335653936, -1.17685839310269)


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=76.0265491372449x_{1} = 76.0265491372449
x2=38.3274576033144x_{2} = 38.3274576033144
x3=52.1504527572588x_{3} = 52.1504527572588
x4=45.8672717555654x_{4} = 45.8672717555654
x5=96.1327395281477x_{5} = 96.1327395281477
x6=65.9734549155131x_{6} = 65.9734549155131
x7=−59.6902491914779x_{7} = -59.6902491914779
x8=42.0973641290712x_{8} = 42.0973641290712
x9=−76.0265352964986x_{9} = -76.0265352964986
x10=18.2213578662666x_{10} = 18.2213578662666
x11=−89.8495449378441x_{11} = -89.8495449378441
x12=−86.0796333100335x_{12} = -86.0796333100335
x13=−55.9203364424288x_{13} = -55.9203364424288
x14=−35.8141250655249x_{14} = -35.8141250655249
x15=86.0796441066858x_{15} = 86.0796441066858
x16=−1.87355407126933x_{16} = -1.87355407126933
x17=82.3097334282055x_{17} = 82.3097334282055
x18=72.2566386939008x_{18} = 72.2566386939008
x19=1.89608744677742x_{19} = 1.89608744677742
x20=−49.6371476919406x_{20} = -49.6371476919406
x21=11.9383327386359x_{21} = 11.9383327386359
x22=−65.9734365352531x_{22} = -65.9734365352531
x23=99.9026503919548x_{23} = 99.9026503919548
x24=−69.7433486862369x_{24} = -69.7433486862369
x25=21.9912312856791x_{25} = 21.9912312856791
x26=39.5840929633375x_{26} = 39.5840929633375
x27=−96.1327308715469x_{27} = -96.1327308715469
x28=48.3805439543555x_{28} = 48.3805439543555
x29=8.16874034587409x_{29} = 8.16874034587409
x30=32.0442840212249x_{30} = 32.0442840212249
x31=−42.0973189870869x_{31} = -42.0973189870869
x32=−99.9026423763554x_{32} = -99.9026423763554
x33=−25.7609994848026x_{33} = -25.7609994848026
x34=−21.9910658633337x_{34} = -21.9910658633337
x35=−15.7078011506911x_{35} = -15.7078011506911
x36=−79.7964471192538x_{36} = -79.7964471192538
x37=55.9203620253561x_{37} = 55.9203620253561
x38=−45.8672337292251x_{38} = -45.8672337292251
x39=−93.6194565131637x_{39} = -93.6194565131637
x40=−11.937771402252x_{40} = -11.937771402252
x41=28.274383917284x_{41} = 28.274383917284
x42=92.3628287043813x_{42} = 92.3628287043813
x43=62.2035448789159x_{43} = 62.2035448789159
x44=−32.0442061118175x_{44} = -32.0442061118175
x45=−5.65361533565394x_{45} = -5.65361533565394
Puntos máximos de la función:
x45=−64.0884998719047x_{45} = -64.0884998719047
x45=70.3716673631468x_{45} = 70.3716673631468
x45=5850.90215804446x_{45} = 5850.90215804446
x45=−71.6283202981817x_{45} = -71.6283202981817
x45=−13.8232170107815x_{45} = -13.8232170107815
x45=6.28217176404258x_{45} = 6.28217176404258
x45=30.1592454981252x_{45} = 30.1592454981252
x45=40.2123612293018x_{45} = 40.2123612293018
x45=54.0353799422805x_{45} = 54.0353799422805
x45=−37.6991399878088x_{45} = -37.6991399878088
x45=−57.8053167968865x_{45} = -57.8053167968865
x45=26.3893208515907x_{45} = 26.3893208515907
x45=50.2654666259918x_{45} = 50.2654666259918
x45=74.141579347988x_{45} = 74.141579347988
x45=−27.6460676867148x_{45} = -27.6460676867148
x45=16.3361319124947x_{45} = 16.3361319124947
x45=67.8583926308789x_{45} = 67.8583926308789
x45=20.1060940355284x_{45} = 20.1060940355284
x45=−52.7787709398789x_{45} = -52.7787709398789
x45=−20.1062919284733x_{45} = -20.1062919284733
x45=−7.54052585811551x_{45} = -7.54052585811551
x45=−3.77272156255489x_{45} = -3.77272156255489
x45=−81.6814149886701x_{45} = -81.6814149886701
x45=−23.8761743338961x_{45} = -23.8761743338961
x45=−74.1415939014473x_{45} = -74.1415939014473
x45=87.9645891310655x_{45} = 87.9645891310655
x45=−67.8584100041957x_{45} = -67.8584100041957
x45=43.982276472445x_{45} = 43.982276472445
x45=−98.0176949554292x_{45} = -98.0176949554292
x45=−80.424778116052x_{45} = -80.424778116052
x45=84.1946774734577x_{45} = 84.1946774734577
x45=98.0176866285732x_{45} = 98.0176866285732
x45=−33.9292354053324x_{45} = -33.9292354053324
x45=23.8760339998439x_{45} = 23.8760339998439
x45=−87.9645994699618x_{45} = -87.9645994699618
x45=5.024964087331x_{45} = 5.024964087331
x45=−54.0354073411945x_{45} = -54.0354073411945
x45=−43.9823178280303x_{45} = -43.9823178280303
x45=10.0527006741872x_{45} = 10.0527006741872
x45=77.9114912194587x_{45} = 77.9114912194587
x45=33.9291659120648x_{45} = 33.9291659120648
x45=64.088480394553x_{45} = 64.088480394553
x45=11.3094208157978x_{45} = 11.3094208157978
x45=89.2212263370942x_{45} = 89.2212263370942
x45=−10.0534922464597x_{45} = -10.0534922464597
x45=−91.734510238114x_{45} = -91.734510238114
x45=94.2477751045297x_{45} = 94.2477751045297
x45=−77.9115043985929x_{45} = -77.9115043985929
x45=−47.7522258763082x_{45} = -47.7522258763082
x45=60.318567954868x_{45} = 60.318567954868
Decrece en los intervalos
[99.9026503919548,∞)\left[99.9026503919548, \infty\right)
Crece en los intervalos
(−∞,−99.9026423763554]\left(-\infty, -99.9026423763554\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
−25cos⁡(5x)+2x3=0- 25 \cos{\left(5 x \right)} + \frac{2}{x^{3}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−60.0044196095073x_{1} = -60.0044196095073
x2=−69.4291976921417x_{2} = -69.4291976921417
x3=16.0221264233968x_{3} = 16.0221264233968
x4=−39.8982264486724x_{4} = -39.8982264486724
x5=−27.960175348931x_{5} = -27.960175348931
x6=98.3318500405323x_{6} = 98.3318500405323
x7=66.2876050456763x_{7} = 66.2876050456763
x8=−49.9513230637031x_{8} = -49.9513230637031
x9=−76.969020048039x_{9} = -76.969020048039
x10=14.1371612783264x_{10} = 14.1371612783264
x11=−21.6769908805772x_{11} = -21.6769908805772
x12=−43.0398195548623x_{12} = -43.0398195548623
x13=−97.7035315094876x_{13} = -97.7035315094876
x14=−102.730079757628x_{14} = -102.730079757628
x15=2.20061623922403x_{15} = 2.20061623922403
x16=46.1814121702195x_{16} = 46.1814121702195
x17=48.0663674558464x_{17} = 48.0663674558464
x18=−11.6239030056985x_{18} = -11.6239030056985
x19=−83.880523823737x_{19} = -83.880523823737
x20=−71.9424718101761x_{20} = -71.9424718101761
x21=80.1106126976605x_{21} = 80.1106126976605
x22=72.5707903397876x_{22} = 72.5707903397876
x23=22.305309282255x_{23} = 22.305309282255
x24=−5.96895080576927x_{24} = -5.96895080576927
x25=−61.8893753432139x_{25} = -61.8893753432139
x26=−85.7654794683633x_{26} = -85.7654794683633
x27=−93.9336203230304x_{27} = -93.9336203230304
x28=36.1283158555771x_{28} = 36.1283158555771
x29=−63.7743308061874x_{29} = -63.7743308061874
x30=44.2964562315334x_{30} = 44.2964562315334
x31=−31.7300863021052x_{31} = -31.7300863021052
x32=−48.0663677440013x_{32} = -48.0663677440013
x33=49.9513233204523x_{33} = 49.9513233204523
x34=61.8893752082239x_{34} = 61.8893752082239
x35=39.8982269525084x_{35} = 39.8982269525084
x36=−75.7123829883794x_{36} = -75.7123829883794
x37=−53.7212342731849x_{37} = -53.7212342731849
x38=−33.615040972181x_{38} = -33.615040972181
x39=68.1725605323985x_{39} = 68.1725605323985
x40=−80.110612635419x_{40} = -80.110612635419
x41=−19.7920316539048x_{41} = -19.7920316539048
x42=−81.995568287717x_{42} = -81.995568287717
x43=38.0132708171541x_{43} = 38.0132708171541
x44=−14.1371726039681x_{44} = -14.1371726039681
x45=−7.85401465912929x_{45} = -7.85401465912929
x46=26.0752199272721x_{46} = 26.0752199272721
x47=88.9070721193584x_{47} = 88.9070721193584
x48=−16.0221186432134x_{48} = -16.0221186432134
x49=−4.08430528610942x_{49} = -4.08430528610942
x50=−70.0575161285199x_{50} = -70.0575161285199
x51=83.8805238779579x_{51} = 83.8805238779579
x52=65.0309679874868x_{52} = 65.0309679874868
x53=−29.8451296072374x_{53} = -29.8451296072374
x54=78.2256570409608x_{54} = 78.2256570409608
x55=−51.8362788991047x_{55} = -51.8362788991047
x56=7.22570551432486x_{56} = 7.22570551432486
x57=71.9424717242364x_{57} = 71.9424717242364
x58=−103.358398317595x_{58} = -103.358398317595
x59=5.96910127218254x_{59} = 5.96910127218254
x60=92.0486647296661x_{60} = 92.0486647296661
x61=−41.783182512083x_{61} = -41.783182512083
x62=−36.1283151769881x_{62} = -36.1283151769881
x63=34.2433595256631x_{63} = 34.2433595256631
x64=−38.0132713997189x_{64} = -38.0132713997189
x65=27.9601738849672x_{65} = 27.9601738849672
x66=81.9955682296702x_{66} = 81.9955682296702
x67=99.5884871025973x_{67} = 99.5884871025973
x68=−92.0486647706958x_{68} = -92.0486647706958
x69=−43.6681376927545x_{69} = -43.6681376927545
x70=21.0486724947694x_{70} = 21.0486724947694
x71=12.2522200481261x_{71} = 12.2522200481261
x72=56.2345085892301x_{72} = 56.2345085892301
x73=54.3495528074409x_{73} = 54.3495528074409
x74=32.3584048042104x_{74} = 32.3584048042104
x75=17.9070753390455x_{75} = 17.9070753390455
x76=−9.73891990454449x_{76} = -9.73891990454449
x77=−87.6504350113946x_{77} = -87.6504350113946
x78=60.0044197576228x_{78} = 60.0044197576228
x79=76.9690199778608x_{79} = 76.9690199778608
x80=−26.0752181223183x_{80} = -26.0752181223183
x81=−3953.69435454276x_{81} = -3953.69435454276
x82=93.9336203616392x_{82} = 93.9336203616392
x83=−58.1194641729107x_{83} = -58.1194641729107
x84=76.3407015181946x_{84} = 76.3407015181946
x85=10.3672413976428x_{85} = 10.3672413976428
x86=−53.0929159525755x_{86} = -53.0929159525755
x87=4.08383553217665x_{87} = 4.08383553217665
x88=−73.8274273195983x_{88} = -73.8274273195983
x89=−65.6592865165505x_{89} = -65.6592865165505
x90=100.216805665411x_{90} = 100.216805665411
x91=−17.9070809118755x_{91} = -17.9070809118755
x92=24.1902623023296x_{92} = 24.1902623023296
x93=88.2787535426163x_{93} = 88.2787535426163
x94=−95.8185759526761x_{94} = -95.8185759526761
x95=90.1637091798556x_{95} = 90.1637091798556
x96=58.1194640099116x_{96} = 58.1194640099116
x97=70.0575162215848x_{97} = 70.0575162215848
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=0x_{1} = 0

lim⁡x→0−(−25cos⁡(5x)+2x3)=−∞\lim_{x \to 0^-}\left(- 25 \cos{\left(5 x \right)} + \frac{2}{x^{3}}\right) = -\infty
lim⁡x→0+(−25cos⁡(5x)+2x3)=∞\lim_{x \to 0^+}\left(- 25 \cos{\left(5 x \right)} + \frac{2}{x^{3}}\right) = \infty
- los límites no son iguales, signo
x1=0x_{1} = 0
- es el punto de flexión

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
[99.5884871025973,∞)\left[99.5884871025973, \infty\right)
Convexa en los intervalos
(−∞,−102.730079757628]\left(-\infty, -102.730079757628\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(cos⁡(5x)+1x)=⟨−1,1⟩\lim_{x \to -\infty}\left(\cos{\left(5 x \right)} + \frac{1}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞(cos⁡(5x)+1x)=⟨−1,1⟩\lim_{x \to \infty}\left(\cos{\left(5 x \right)} + \frac{1}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(5*x) + 1/x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡(5x)+1xx)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(5 x \right)} + \frac{1}{x}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(cos⁡(5x)+1xx)=0\lim_{x \to \infty}\left(\frac{\cos{\left(5 x \right)} + \frac{1}{x}}{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:
cos⁡(5x)+1x=cos⁡(5x)−1x\cos{\left(5 x \right)} + \frac{1}{x} = \cos{\left(5 x \right)} - \frac{1}{x}
- No
cos⁡(5x)+1x=−cos⁡(5x)+1x\cos{\left(5 x \right)} + \frac{1}{x} = - \cos{\left(5 x \right)} + \frac{1}{x}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор