1997考研数学三试题及解析.pdf

1997 f x 1y f ln x e ( ) f dy _________________. ( ) f x ⎡1 ⎤ e ( ) f ′ ln x + f ′ x f ln x dx ⎢ ( ) ( ) ( )⎥ ⎣x ⎦ f x f x f x dy d ⎡f ln x e ( )⎤ ⎡df ln x ⎤⋅e ( ) + f ln x de ( ) ⎣ ( ) ⎦ ⎣ ( )⎦ ( ) ⎡1 ⎤ f x f x f ′ ln x dx =⋅e ( ) +f ln x e ( ) ⋅f ′ x dx ⎢ ( ) ⎥ ( ) ( ) ⎣x ⎦ ⎡1 ⎤ f x f x f ′ ln x dx =⋅e ( ) +f ln x e ( ) ⋅f ′ x dx ⎢ ( ) ⎥ ( ) ( ) ⎣x ⎦ 1 2 1 1 2 f x =+ −x f x dx f x dx _______________. ( ) 1+x 2 1 ∫0 ( ) , ∫0 ( ) π 4 −π 1 f x dx A, ∫0 ( ) 1 1 dx 1 2 A f x dx +A ⋅ 1−x dx ∫0 ( ) ∫0 1+x 2 ∫0 1 A 2 1 π π arctan x 0 =+ ⋅(arcsin x +x 1−x )0 =+ A 2 4 4 π A . 4 −π 3 t y t +1 −y t t 2 y t ____________. C + t −2 2t ( ) y t +1 −y t 0 C.C t t (at +b )2 y t +1 −y t t 2 a 1,b =−2. y C =+ t −2 2t . t ( ) 4 f (x , x , x )