6 + a lim = 8, a =. a l. a a + a a a a lim = lim + = e, a a a e = 8 a= l ( 6,, ), 4 y+ z = 8. + y z = ( 6,, ) 4 y z 8 a ( 6,, ) + = = { } i j k 4,,, s = 6 = i+ j k. 4 ( ) ( y ) ( z ) + y z =. + =, () y y + y = e. y = Ce cos + Ce si + e λ λ+ =, s = ; λ, = ± i, α = y * Ae * =
A =, 4 u l ( y ) z = + + (,,) y = Ce cos + C e si + e A A.. AB,,, u AB 5 A 4. B u = =, A (,,) + y + z u y = = y A (,,) + y + z y + z u z = =, z A (,,) + y + z y + z cos α =,cos β =,cos γ =, u = + + = AB A r( A) =, = =, B r( AB)= r( A ) =, =, r AB. B = ( + ) + ( + y) ay d ydy a A -. B. (C). (D).
D. ( + ) + ( + y) ay d ydy ( a ) ay y ( a )( y) y + ay ( + y) y ( + y) =, =. a = D. A B.. =, =,lim =, C (, ) y =. D (, ) y = B. lim = =.. ( ξ ) = + + ξ! ( ξ ) = +! a ( ) B > =,,, = a λ,, λ ta a = A. (C). A. B. D λ.
λ λ ta a = ta a, lim ta = λ, λ λ ta a < ( λ + ) a a a = = λ ta a A 4 = = = ( ) () F k k,, F t t dt, C. = = + F t dt t t dt t dt = t dt. () F k =,, F lim lim lim () t dt = = k k k ( ) k ( k ) k = lim = lim, k ( k ) k = C. a b a b 5 b a b a 4 4 A aa 4 bbbb 4. B aaaa 4 + bbbb 4.
C ( aa bb )( aa bb ) D ( aa bb)( aa bb) 4 4. 4 4. D a a b b a b D. b a 4 4 a b a b a b a b b a a b 4 4 a b a b = aa bb 4 4 b a b a ( aa bb)( aa bb) = 4 4. r a( cosθ ) = + a >. θ r θ = asi θ, ds= r θ + r θ dθ = a cos dθ cos θ 8 si θ s = a dθ = a = 8 a ( ) =, = 6 + =,,, { }. + =, = 6 + = 4 k k > k + >. = 6+ > 6 + =. k+ k k+ k+,, > + { }. > ( =,, ), { } { }. lim = a, = 6 + + a= 6 + a, a a 6= a = a = >
a =. z. S Oy + z dydz + zddy, S z = + y ( z ) s = +, D S z z ( y ) ( ) ( ) ( ) + z dydz + zddy = + z dydz + zddy + z dydz + zddy s S+ S S ( ) = + dv ddy Ω = + =. z =, z y = y r = dθ rdr dz D ( ) ( ) ( ) s + z dydz + zddy = z z z + + ddy S ( 4 ) = z + z ddy S = 4 + + + D y y ddy = dθ 4r cos θ r cosθ + r =. S yoz D yz = z y, z, D S Oy y = z y, z,
s ( ) + z dydz + zddy ( ) ( ) = z y + z dydz + z y + z dydz + + y ddy Dyz Dyz Dy = 4 + + Dyz z y dydz y ddy Dy θ y = 4 dy z y dz + d r rdr =. u = y z z z z 6 + = =, a. v = + ay y y uv z z z z z z = +, = + a, u v y u v ( a) ( a a ) z z z z = + +, u u v v z z z z = + ( a ) + a, y u u v v z z z z = 4 4 a + a. y u u v v 5 z z + + 6 + = uv v a a =. + = + 5a, 6 a a, = ( ) S. = =,
= ( ) = =, l, S = = = = = + + = = = + =. = = S = l ( ) + + + l ( )( <, ), 4 5 S = = l. 8 4 = ( ),. tdt, > y = (, ) Y () y =, Y = X X = Y = ( tdt ) ( ) ( ), = tdt= = ( ) = C, + = = C + C( C C ) l. [,], c (,) a b a b
b ( c) a+. = c = ( c) + ( c)( c) + c! ξ = c+ θ( c), < θ<. * =, ( ξ ) ( * ) ( ξ ) = ( c) + ( c)( c) + c, < ξ<c<,! ( *) = ( ξ ) = ( c) + ( c)( c) + c, < ξ <,! () = ( c) + ( ξ)( c) ( ξ) c! (,) ( c) = () ( ξ)( c) ( ξ) c () + + ( ξ ) ( c) + ( ξ ) c b a+ ( c) + c. c c + c, b c a+. A A= E ξξ E ξ ξ ξ = A ξ ξ = ; ξ ξ = A. ξξ ξξ ξξ ξ ξ ξ ξ ξ ξ ξξ, A = ( E )( E ) = E + = E ( ) A = A E ( ξ ξ ) ξξ = E ξξ ( ξ ξ ) ξξ =
ξ, ξξ A = A ξξ= ; ξξ= A= E ξξ, Aξ = ξ ξξ ξ = ξ ξ =, ξ, A = A = A. ξξ= A A A( E A) = =, E A A = E A= ξξ, A = ( A) < A.. A ξξ =, A A A = A A, A= E. ξξ = A A= E E A.,, = 5 + 5 + c + 6 6. () c (),, =. 5 A = 5. c ( A) =, A =, c =, A. λ 5 λe - A = λ 5 = λ( λ 4)( λ ), λ λ λ λ =, = 4, =.,, =. A B A B 6 4
A.. 7 A ={ A } B { B } C { }, P A =.6, P B =.4, P C A =., P C B =., ( ) P A C ( ) ( ) + ( ) P AC P A P C A = = P C P A P C A P B P C B.6. =.6.+.4. =. 7 () ξ, η E ( ξ η ) =. N, ξ η. ξ, η Z ξ η N,, E Z = Eξ Eη =, D Z = Dξ + Dη = + =, = Z ~ N (, ). ( ξ η ) + E = E Z = z e dz + z = e d =. ξ, η ξ P i, i,,, { ξ = } = = X = ( ξη) Y = ( ξη) ma,, mi,.
( X, Y ) Y X () X E( X ). X = ma ( ξ, η), Y = mi ( ξ, η). P{ X Y} { } P X =, Y = = P X =, Y = = P X =, Y = =, P{ X =, Y = } = P{ ξ =, η = } = P{ ξ = } P{ η = } =, P{ X =, Y = } = P{ ξ =, η = } = P{ ξ = } P{ η = } =, P X =, Y = = P =, = = P = P = =, { } { ξ η } { ξ } { η } P{ X =, Y = } = P{ ξ =, η = } + P{ ξ =, η = } = + =, P{ X =, Y = } = P{ ξ =, η = } + P{ ξ =, η = } = + =, 7 P{ X =, Y = } = = ; < = Y X X
X P 5 X 5 E( X ) = + + =.