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2006

4 4 16 .

1. x −→0 α=+ x

0cos t dt , β=2 x 2

0tan √, γ= √0sin t 3dt

A α,β,γ; B α,γ,β; C β,α,γ; D β,γ,α

2. f (x ) f (0)>0 δ>0

A f (x ) (0, δ) ;

B f (x ) (−δ,0) ;

C x ∈(0, δ) f (x ) >f (0);

D x ∈(−δ,0) f (x ) >f (0)

3. {a n }, {b n }, {c n } lim n →∞a n =0, lim n →∞b n =1, lim n →∞c n =∞,

A a n

B b n

C {a n c n } ;

D {b n c n }

4. f (x, y ) (x 0, y 0)

(A)f (x 0, y ) y =y 0 ;

(B)f (x 0, y ) y =y 0 ;

(C)f (x 0, y ) y =y 0 ;

(D)f (x 0, y ) y =y 0

8 3 24 .

1. lim x →0(cosx ) 1/ln(1+x ) =(

3.

( ∞2) ) −|b k |) ∞n =1b n 2. z =x 2+y 2 2x +4y −z =0 (n =1a n ∞k =100(a k )

) 4. f (e x ) =xe −x f (1)=0 f (x ) =(

1