2000考研数学二试题及解析.pdf

2000 arctan x −x 1lim . x →0 3 ln 1+2x ( ) 1 − . 6 1 −1 arctan x −x arctan x −x 1+x 2 lim lim lim x →0 ln 1 2 3 x →0 2x 3 x →0 6x 2 ( + x ) 2 −x lim x →0 6x 2 (1+x 2 ) 1 =− 6 2y y x 2xy x =+y dy . ( ) | x 0 ln 2 −1 dx ( ) 2xy (ydx +xdy )ln 2 dx =+dy x 0 y 1 ln 2dx −dx dy, dy ln 2 =−1 dx, | ( ) x 0 2xy x =+y x xy ⎛ dy ⎞ dy 2 ln 2 ⋅ y +x 1 =+ ⎜ ⎟ ⎝ dx ⎠ dx x 0 y 1x 0 y 1 dy ln 2 1+0 1=+ ( ) dx dy ln 2 =−1 dx dy ln 2 =−1 dx, | ( ) x 0 +∞ dx 3∫2 (x +7) x −2