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4111,0(),0xxfxxabxx⎧−−⎪=⎨⎪+≥⎩0x=a=b=()21arctanelne12xxyx=−++1ddxyx==()yyx=sine02xxyyπ++=(0)y′=22e(2)xyx=−()arcsinfxx=Peano3Maclaurin0x→xxxxf5sin3sin2sin)(+−=x.lim()xafx→=∞lim()xagx→=∞[]Alim[()()]xafxgx→+=∞Blim[()()]xafxgx→−=∞C1lim0()()xafxgx→=+Dlim()xakfx→=∞kf[0,1]()0fx′′[]A(1)(0)(1)(0)ffff′′−B(1)(1)(0)(0)ffff′′−C(1)(0)(1)(0)ffff′′−D(1)(0)(1)(0)ffff′′−Af0xf0x42Bf0xf0xC[,)fCab∈f(,)ablim()xafxk+→′=kfa()fa+′()lim()xafafxk++→′′==Dyfg=o(),()yfuugx==g0xf00()ugx=yfg=o0x2211lim1sinnnnnn→∞⎛⎞++⎜⎟⎝⎠.()2240e1limsin2xxxx−→−+.f(0)3,(0)1ff′′′==()3()e1txftyfπ=−⎧⎪⎨=−⎪⎩0ddtyx=202ddtyx=.4322()cosfxxx=()()(3)nfxn≥111e()23exxFx+=−.02xπ2sintan3xxx+442()fxaxbxc=++(,,abc)1x≤()1fx≤1x≤()4fx′≤.[0,1]fC∈(0,1)(0)(1)0ff==[0,1]max()0xfxM∈=1n1ξ,2(0,1)ξ∈1211()()nffMξξ−=′′.