考研数学历年试题详解及评析(1995-2009).pdf

1995 2 (1) lim 1+3x sin x . ( ) x →0 6 e . 1 : 6x 2 1 sin x ⎧ ⎫ 6 lim 1+3x sin x lim 1=+3x 3x e . ( ) ⎨( ) ⎬ x →0 x →0 ⎩ ⎭ 2 : 6ln 1+3x 2 lim 2 ln 1+3x lim ( ) sin x x→0 sin x ( ) x→0 3x 6 lim 1+3x e e e . ( ) x →0 d 0 2 (2) dx ∫x 2 x cos t dt . 0 2 2 4 cos t dt −2x cos x . ∫x 2 d 0 2 d 0 2 0 2 2 2 x cos t dt x cos t dt cos t dt +x cos x −2x dx ∫x 2 dx ( ∫x 2 ) ∫x 2 ( ) ( ) 0 2 2 4 t dt =− x x cos 2 cos . ∫x 2 (3) a ×b ⋅c 2, ⎡ a +b × b +c ⎤⋅ c +a . ( ) ⎣( ) ( ) (⎦ ) 4. ⎡ a +b × b +c ⎤⋅ c +a ⎣( ) ( ) (⎦ ) a =+b ×b ⋅ c +a + a +b ×c ⋅ c +a ⎡⎣( ) ⎤⎦ (