高等数学A,B上册期中卷 7

2290507AB2005AB.54201.22limsin1xxxx→∞=+2.0x→,()1arcsincosxxxxα=+−2()xkxβ=,k=3.()1sinxyx=+dxyπ==4.()exfxx=1x=PeanoTaylor5.32esin,0()2(1)9arctan,0xaxxfxbxxx+=−+≥a=b=.44166.11()1exxfx−=−[]A0,1xx==()fxB0,1xx==()fxC0x=()fx1x=()fxD0x=()fx1x=()fx7.()yyx=22ln(1)xttyt=+=+()yyx=3x=x[]A1ln238+B1ln238−+C8ln23−+D8ln23+8.[]A()fx′(0,1)()fx(0,1)B()fx(0,1)()fx(0,1)C()fx′(0,1)()fx(0,1)D()fx(0,1)()fx′(0,1)2309.a32()2912fxxxxa=−+−[]A2B4C6D8.573510.011lim1exxxx−→+−−11.()3limln12ln1xxx→+∞++12.111lim12nnnnn→∞++++++13.1(),(12)fxxx=−()()nfx14.()yyx=222sin()e0xxyxy++−=ddyx.42915.6350cm5cm16.712e1e(0)xxxx−≥+≥17.8214yx=21,4Paa(0)aPQQP18.8()fx[],ab(),ab()fab=()fba=1(),cab∈()fcc=2(),,abξη∈()()1ffξη′′⋅=2006AB.458241sin()(1)xfxxx=−221lim01xxaxbx→∞+−−=+a=b=3arctan()yfx=()fxdy=23143,1(),1axbxfxxx+=≤()fx1x=a=b=510x=0x→20x=0x=30x=00x=400∞∞.4121()fx()gx()()(),()ffxfgx()()(),()gfxggx[](A)()()(),()ffxfgx(B)()()(),()gfxggx(C)()()(),()fgxgfx(D)()()(),()ggxffx20x→2ln(1)yxaxbx=+−−2x[](A)11,2ab==(B)11,2ab==−(C)11,2ab=−=(D)11,2ab=−=−3[](A)0(1,2,)nxn≥={}nx{}nx0a(B)0(1,2,)nxn={}nx0a(C)lim0nnxa→∞=≥0(1,2,)nxn≥=(D)lim0nnxa→∞=NnN2nax.73510sinlim(1cos)ln(1)xxxxx→−−+2.212lim1xxxx−→∞−+3()2arctanln1xttyt=+=+2112dd,ddttyyxx==.4.23exyx=(10)()yx.5.()yyx=22e2xyxyy+−=()yyx=(0,2).232.810112,2,(1,2,)2nnnxxxnx−−−==+=+}{nx..80x≥,()()22(1)2ln(1)114arctan2ln1xxxxx++−+≥−+..(7)()fx[0,1](0,1)(0)0f=(0,1)ξ∈3()()1ffξξξ′=−(6)1()arctan1nfxxxn=−+(n)1()nfx(0,)+∞(0,)nx∈+∞()0nnfx=21limnnnxx+→∞.2007AB.4241n→∞111kknn−−1cos(0)aan−k=a=221lim01xxaxbx→∞+−−=+a=b=31()1xfxx−=+Peano4Maclaurin4222esindd31xxxπ−++=+(______________________________________)5yx=0M,xy0M621()lnfxxx=_________________________..4127x∀∈R,()()()hxfxgx≤≤,lim[()()]0xgxhx→∞−=,lim()xfx→∞[](A)(B)(C)(D)82141ln1lim2sinxxxxx→−∞+++=−+[]233(A)2−(B)2(C)3−(D)393()sinfxxxx=−[](A)0(B)1(C)2(D)3.8321001sincoslimsinln(1)xxxxxx→+−⋅+11.32ln(1)xttytt=−+=+22ddyx.12()2()sin2fxxxx=+(10)()fx.13.ab2yxaxb=++321yxy=−+(1,1)−.(14).82333()lim(0)2nnnnxfxxx+→∞=≥+.(15).8()fx(,)−∞+∞(0)1f′=,xh,()()()2fxhfxfhhx+=++,()fx(,)−∞+∞,()fx′.(16).(8)1p,1q,111pq+=0x11pxxpq+≥(17)(8)()fx[,]ab(,)ab()()fafb=()()0fafb+−′′(,),abξ∈()0fξ′′=.2005AB.94361.22060sindlimxxttx→=∫2.322(1)xyx=+3.()yyx=lnlnyyx=ddyx=2344.f[0,]π0()sin()dfxxfxxπ=+∫()fx=5.21,0()e,0xxxfxx+=≥31(2)dfxx−=∫6.2sindcosxxxxππ−=+∫7.lnyx=13x≤≤8.1exy−=22exy=0yayby′′′++=a=b=9.0()0fx′′=()yfx=00(,())xfx.47281.220()sindxfxtxtt=−∫()fx′2.2e1de4xxx−+∫3.240sinsindxxxxπ−∫4.21d221xxxx+∞−+∫.92:(0,0)yabxabΓ=−ab1Γ1yx=−+2Γxy.2141.6()222e1ded0xxxyxy−+=2.822exyyx′′′−=+9(0)2,(0)4yy′==.71eulnxxu=ex()xu2u→+∞1()xulnuu.6111ln2111ln213521nnn++++++−−n12352006AB.94361200edlim(cos1)xtxxtxx→−=−∫2231xtyt=+=2t=3()ln(1)fxxx=−+4()yyx=ln1xyy−=(0)y′=5512224111d1xxxxxxx−−−+−=++∫6)(xf201(2)darctan2xtfxttx−=∫1)1(=f,21()dfxx=∫7)(xyy=xα++∆=∆21xxyy0→∆xαx∆π=)0(y_____)1(=y81lneyxx=+9312e,exxyy==..472812arccosdxxxx−∫220sindxxxπ∫3()211d1xxx+∞+∫431()d1xtGxtt=+∫10()dGxx∫7lncos1sin2xtyt==0t=4tπ=21729161()2sincotyyxyx′=−2sinyyxx′′+=+32yx=23671a≤121()edxIaxax−=−∫6)(xf]4,2[0)3(=f]4,2[∈ξ42()3()dffxxξ′′=∫2007AB55()22yyxxππ=2200edcosd0yxtttt−=∫∫()yx62exyx−=7.2222lim3123nnnnnnnn→∞+++=+++8()231cos2cossindxxxxππ−++=∫.37211022202dxxxx−∫11.()arctan1dxx+∫122ecosdxxxπ+∞−∫13820e,()0,xxxfxxx≥=221e,02()10,2xxFxxx≥=..94361()210limexxxx→−=21sinxyx=dy=3(3)2f′=0(3)(3)limsin2hfhfh→−−=4eθρ=2πθ=92sinyyx′′+=*y=.2371)(xF)(xf),(∞+−∞2()dfxx∫.1472sin()()dxxxtfxtt=∫20()limxfxx→.156(cossin2)dd0yxxxy+−=.168()fx()gx()(),()2e()xfxgxgxfx′′==−(0)0,(0)2fg==20()()d1(1)gxfxxxxπ−++∫.178)10(=aaxy2yx=1S1x=2S.1a12SS+.2x.18612()sindxxfxtt+=∫0x1()fxx.