2020年中国科学院大学硕士研究生（考研）入学考试试题数学分析.pdf

?2020?1.?150?180?2.?1(?15?)?limx051 + 3x41 2x31 + x 1 + x.2(?15?)?x0= ,x1= ,xn+1=23xn+13xn1(n 1).?xn?3(?15?)?limx01xZsinx0sin1xcost2dt.4(?15?)?f(x)?0,n(n?)?f(0) = f(n),?x0 0,n1?f(x0) = f(x0+1).5(?15?(1)?8?(2)?7?)?(1)I1=Z10 xb xalnxdx(a,b 0).(2)I2=Z10ln(1 + x)1 + x2dx.6(?15?)?D?Oxy?y =x?y = x?D?y = x?7(?15?)?f(x,y,z) = lnx + lny + 3lnz?x2+ y2+ z2= 5R2(x,y,z 0)?8(?15?)?32 Z10rx2 x + 1x x2dx .9(?15?)?Pn=12 + (1)nnxn?10(?15?)?Z200100 x3x4+ x 1dx ln2?13 106.?1?1?