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胜樊
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1 lim =.. ( + + ) ( ) = lim ( ) = lim = lim =. lim + + = lim + = lim lim + =. ( ) ~ 3 ( + u) λ.u + = o = o ( ) λ λ λ + u = + λu+ u + o u,,,!

2 + + + o( ) lim 8 8 o( ) = lim + = 3 y = + + A = y =, y() =, ( ) ( ) A= + + d+ + + d 3 3 = = l si 3 d =. si cot l si cot + C. l si d = l si d ( cot ) cot l si cot d si = + = cot l si + csc d = cot l si cot X + C d tf t dt d =. f f ( ). u = t, dy = tdt, t = u = ; t = u = d d d d ( tf t ) dt = f ( u) du = f ( ) 5 y = l e+ ( > ).

3 y = + e l e+ a = lim = lim l e+ =, + + b= lim ( y a) = lim l e l e + = lim = lim = + + e + e y = +. e y lim y =, A y. B y. C y. D y. D lim y = lim ( y) lim =, D. y = A

4 y B k, = k = =, = k, = k = = k, = k ( k,, ) ( k,, ) C = y C. D. 3 f = A3. B. C. D. C. 3 = ( ) = ( )( + ) ( )( + ) f, f =, = f. 3 y y y ( ) e y = y = +α, α + y = () A. B. C. D A. y y = +α, + y y = + y y = e = e. () arcta y y α = + +. =, y = e arcta e f = a f ( a) δ > ( δ, δ ) a a+ A( a) f f ( a).

5 B( a) f f ( a). () f t f C lim t a t () f t f D lim t a t C ( a) ( a) ( a δ, a δ ) f f ( a) f f ( a) a δ a < < ( a) f f ( a). a a δ < < + ( a) f f ( a). AB. CD () lim f t f = f a f, t a C. 5 A ( 3) * * ( ka ) =. + ( a δ, a δ ) + A k k, ± A ka * B k A * B A C k A * D k A * * * AA = A A= A E A = AA * ka = ka ka = k A A k = k A A * = k A *

6 B k, ± 3. A A ( aij ) * = a ij ij i j = (,,,, ) ij (,,,, ) = = k Aij i j * ( ka ) = k A * A ij ka ( kaij ) = f = + (, ). ta (, ) ta (, ) =,,,. = lim f =+, + 5 t = f = 5 3 ta lim =+, 5 + t f = f. lim =, 3 + t 7 = 7 f. 7 = 7 f 3 5 7,,, = f. a si abc,, lim = c c 3 l ( + t ) dt t

7 a si, 3 l + t lim dt, = b. b t b >, ( ] ( 3 l + t ),b ( 3 l + t ) b t > b < [,) > t a si a cos a cos lim = lim = lim. 3 3 l ( ) l ( ) + t + dt t a a = c = a=, b=, c= u y = y cos y si + 3ycos = e. cos u = ycos u = y cos ysi, u = y cos y si ycos. u + u = e e u = Ccos + Csi + 5 cos e y = C + Csi + cos 5cos

8 y = usec, = sec + sec ta y u u = sec + sec ta + sec ta + sec 3 y u u u u u + u = e. 3 d. d d d, 3 3 = + d d = lim ε + ε d + ε ( ) = lim arcsi = 3 3 = lim + ε + ε ε = lim l + + ε = l d = + l + 3 d 3 + ε y v.. m, B, ρ, k( k > ). y v

9 y = y( v). OOy, v = dy. dt dy v, dt = d y = dv dy = v dv, dt dy dt dy d y = ρ, m mg B kv dt dv mv = mg Bρ kv, dy mv dy = dv, mg Bρ kv ( Bρ ) l ( ρ ) m m mg y = v mg B kv + C k k v =, y= ( Bρ ) m mg C = l ( mg Bρ kv), k ( Bρ ) m m mg mg Bρ kv y = v l. k k mg Bρ y = f [,]. (, ), [ ] y = f., f (,) f ϕ = f ( t) dt, f [, ] f >. ϕ [,] (,)

10 ϕ( ) = ϕ =.,, ϕ = f f t dt =. f = f d. F f f t dt, = F f f f f f = + + = >, F (,). ϕ =. F = = y =., (, ) y = y = (,) = ( ) =, y = y = ( ) (,) y = ( ) S = y + y d= 3d 5 5, = 6 y =

11 5 S = d= 5 S = S+ S = 5 6 y y = (, y) + y (,) y y < = + y y =. y = ( + y ). y ( + y ) = + y 3,, y =, y = + y =,. ( y ) y = +. y( ) =, y ( ) =, y = p, y = p, ( p ) p = +, arcta p = C p = C = arcta = ta y = p=

12 y ( ) =, y = ta d= l cos + C C = + l, y = l cos + + l = + 3 y l cos l,, = + + cos, y 3 +. = y y = + l. (,) + + < l ; l < l <. + ϕ = + + l ; ϕ ϕ ϕ ( ) =, ϕ l + + l +, =. = l +, + l( + ) = <,, < = <,, + ϕ ϕ ϕ ϕ ϕ ϕ <,

13 ϕ <, + + < l, f =,, l ( + ) f = ( + ) l ( + ) ( + ) l ( + ) () f ( ) < (,).(,) f. f (,] f () =. l (,). f (,). = l > l ( + ) ( + ) lim+ ( + ) l + l + lim f = lim = lim l = = f = l > ( + ) T ( E C B) A = C, E A T A. 3 3 B=, C = A.

14 T C E C B A E, = 3 3 C B=, C B =, C B. T T A= ( C B) = ( C B) C B A T = E. = = 3 3 T T T α = (,,, ), α = (, 7,,3 ), α = (,,, a), β = ( b ) 3 ab, β α α α 3 ab, β α α α A ( α, α, α3 β) = = b b 3 a a 3 a b b ( α, α, α ) 3 β α, α, α 3 3 = β b=, a ( α, α, α ) = β (,, ) T (,,) = = 3 β T 3,,, T β = α + α

15 b=, a= ( α, α, α ) = β 3 (,, ) (,,) (,,) 3 T T T = = k + k β α, α, α 3 ( ) β = k+ α + k+ α + kα k 3

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untitled arctan lim ln +. 6 ( + ). arctan arctan + ln 6 lim lim lim y y ( ln ) lim 6 6 ( + ) y + y dy. d y yd + dy ln d + dy y ln d d dy, dy ln d, y + y y dy dy ln y+ + d d y y ln ( + ) + dy d dy ln d dy + d 7.