第二届全国大学生数学竞赛预赛试题

22(1)(1)(1)nnxaaa=+++||1alimnnx→∞21lim1xxxex−→∞⎛⎞+⎜⎟⎝⎠0s0sxnnIexdx−+∞=∫1,2,n=()ft22rxy=+1(,)gxyfr⎛⎞=⎜⎟⎝⎠2222ggxy∂∂+∂∂10:0xylz−=⎧⎨=⎩2213:421xyzl−−−==−−()fx(,)−∞+∞()0,lim()0,lim()0xxfxfxfxαβ→+∞→−∞′′′′==0x0()0fx()0fx=(,)−∞+∞()yfx=22(1)()xtttytψ⎧=+−⎨=⎩2234(1)dydxt=+()tψ()ytψ=22132tuyedue−=+∫1t=()tψ0na1nknkSa==∑1α1nnnaSα+∞=∑1α≤()nSn→∞→∞1nnnaSα+∞=∑l(,,)αβγ2221αβγ++=2222221xyzabc++=0cbal(,,)αβγ()xϕC422()Cxydxxdyxyϕ++∫vL22(2)1xy−+=422()0Cxydxxdyxyϕ+=+∫v()xϕC422()Cxydxxdyxyϕ++∫v