III http://www.manabino-academ.com
. = k...................................... = k p + q................................. = a + b c + d.................................. 4.4.......................................... 5.5.......................................... 6.6.................................... 7.7............................................. 9.8.................................... 0.9.............................................. = a..................................... = a( p)................................ 5. = a + b + c............................... 6.4.......................................... 7.5.................................... 9.6..............................................7.....................................8.................................... 5 7................................................ 7........................................... 9........................................ 0.4.............................................5.........................................6............................................. 5 4 6 4............................................... 6 4........................................ 7
http://www.manabino-academ.com = a + b c + d 0. = k = k (k \= 0) = 0 = 0 k > 0 k < 0 4 ( i ) k > 0 ( ii ) k < 0 k k k k () = () = () ()
http://www.manabino-academ.com. = k p + q = q = k p + q k p = k p, q = k p q = k p + q (p, q) = p, = q (p, q) k > 0 k < 0 () = + () = + = k p + q (p, q) = q = p = k () = + = =, = () = + = =, = 4 5 5
http://www.manabino-academ.com () = + () = 4 5
http://www.manabino-academ.com 4. = a + b c + d = a + b c \= 0, ad \= bc c + d ( a + d ) ad a + b c + d = c c + b bc ad ( c + d ) = a c + ( c c + d ) = c c bc ad c + d c + a c = k p + q () = () = + + () = + = + ( + ) = + = + + = + = =, = () = + = + = ( ) + = = + = =, = () = () = 5 + +
http://www.manabino-academ.com 5.4 0 = k + q (k \= 0) \= p p = p, = q \= q q p 4 = ( ) = = = ( ) + = + = = = ( ) = = = = =, =, 4 () = ( ) () = + ( )
http://www.manabino-academ.com 6.5 = k + q (k \= 0) = p, = q p = p, = q = k p + q p, q k 5 = a + b =, = (, 5) a, b, + c c =, = = k ( ) + (k \= 0) (, 5) k + + = 5 k = 5 = k \= 0 = + + + ( + ) = + = + 9 + = a + b + c a =, b = 9, c = 5 = a + b ( + c, a, b, c ) =, =
http://www.manabino-academ.com 7.6 { = f() = g() f() = g() 0 6 () =, = + () =, = () =, = +, = + + = + = 0 ( )( + ) = 0 =, (, ), (, ) () 4 =, = 4, 4 = = + + = 0 = ( ) ± ( ) ( ) = ±
http://www.manabino-academ.com 8 ( +, + ), (, ) 6 () =, = + 4 () = 4 +, =
http://www.manabino-academ.com 9.7 0 0 7 () = () 6 + 4 = + () 0 () 0 \= \= 4 = = 0 ( )( + ) = 0 = ( ) =, =, 6 + 4 = + 6 = ( )( + 4) + 4 + 6 = 0 + + = 0 ( + )( + ) = 0 =, =, 7 () = () + = 7 + 7
http://www.manabino-academ.com 0.8 f() > g() (f() g() ) = f() = g() 8 () > + () () =, = +,, = + + = + = 0 ( )( + ) = 0 =, <, 0 < < () =, = 4, 4 4, 4 = = + = 0 = ( ) ± ( ) ( ) = ± 4 <, +
http://www.manabino-academ.com 8 () + + 4 () 4 <
http://www.manabino-academ.com.9 A B > 0 A, B 9 () > () 6 + 4 + () > > 0 ( ) > 0 > 0 ( )( + ) < 0 + 0 + + + + + 0 + + + 0 + P 0 + 0 + P <, < < () 6 + 4 + 6 + 4 + 0 6 + ( )( + 4) 0 + 4 + + 0 + 4 ( + )( + ) 0 + 4 4 + 4 0 + + + + + + 0 + + + + 0 + P + 0 0 + P < 4, 9 () () + > 7 + 7
http://www.manabino-academ.com = a + b 0. = a = a (a > 0) = a = a = a = a = ± a = a = a 0 = a = a = a = a = a = a 0 () = () = () = (4) = () 0 4 0 4 8 0 6 4 () 0 8 4 8 4 0 4 6 0 () 8
http://www.manabino-academ.com 4 () 0 8 0 8 0 6 4 4 () (4) 0 8 8 0 4 6 0 4 ()
http://www.manabino-academ.com 5. = a( p) = a( p) = a p = a p = a( p) (p, 0) a > 0 p a < 0 p () = () = ( + ) = a( p) (p, 0) = a () = = () = ( + ) = 4 6 4 7 5 () = ( ) () = ( + )
http://www.manabino-academ.com 6. = a + b + c = a + b + c (a \= 0) a c = = a a ( + b ) a + b a, c = a + b + c = a b c a () = () = + 4 + = a + b + c () = = ( ) = ( b a, c ) = a () = + 4 + = ( + ) + = 5 7 6 () = + 6 () = 4 +
http://www.manabino-academ.com 7.4 0 = a + b + c a > 0 b a a < 0 b a A A A 0 A 0 c a + b 0 b a a + b + c c c 4 () = ( 0) () = + 4 + (0 4) () = ( 0) = = ( ) = = 0 = 0 = () = + 4 + (0 4) = 0 = 0 + 4 + = = 4 = 4 + 4 + = + + + 4
http://www.manabino-academ.com 8 4 () = + 6 ( ) () = 4 + ( 4 0)
http://www.manabino-academ.com 9.5 { = f() = g() 5 f() = g() () = +, = () =, = () = +, =, + = + = = 0 ( )( + ) = 0 =, = (, ) () =, =, = = + = 0 ( )( + ) = 0 =, = (, )
http://www.manabino-academ.com 0 5 () =, = 8 () = 4, = +
http://www.manabino-academ.com.6 A = B A = B = = ± A = B = A = B B 0 = A = B B 0, A = B 0 A 0 B 0 A = B A = B 0 A 0 6 () + = () = () + = 0, + = = 0 ( )( + ) = 0 =, =
http://www.manabino-academ.com () = 0, = ( ) + = = 0 ( )( + ) = 0 =, = 6 () + 8 = 0 () 4 + =
http://www.manabino-academ.com.7 { = f() = g() f() = g() f() = g() = f() = g() 7 k + = + k = +, = + k k k + = + k + = ( + k) k + k + k = + + (k ) + k = 0 D D = (k ) 4(k ) = 4k 4k + 4k + 4 = 4k + 5 D = 0 4k + 5 = 0 k = 5 4 (, 0) 0 = + k k =
http://www.manabino-academ.com 4 k < 5 4 k <, k = 5 4 k > 5 4 0 7 k = + k
http://www.manabino-academ.com 5.8 f() > g() (f() g() ) = f() = g() 8 () + > () < () = +, =, + = + = = 0 ( )( + ) = 0 =, = = < () =, =, = = + = 0 ( )( + ) = 0 =, = =
http://www.manabino-academ.com 6 < 8 () + 8 () 4 +
http://www.manabino-academ.com 7. = = = f() = = = g() g() f() f () f ( i ) = f() = g() ( ii ) = g() () = + () = + () = 4 + () + = = = = () ( + ) = + = ( ) = = + = +
http://www.manabino-academ.com 8 () + = log 4 = log 4 = log 4 () = () = log ( + ) () = +
http://www.manabino-academ.com 9. = f() P(a, b) b = f(a) a = f (b) Q(b, a) = f () P(a, b) Q(b, a) = = f () = f() = = f () = Q(b, a) = f() P(a, b) () = 4 + () = () 4 + = 4 = = 4 + = = 4 4 = 4 4 4 = 4 4 4 () = = = log = log = log () = + () = log 4
http://www.manabino-academ.com 0. f() f () f() f () () = + (0 ) () = () = ( ) (4) = + ( 0) () = + (0 ) = 0 = 0 + =, = = + = 7 7 = + 7 = + = = ( 7) () = 0 = = + = 5 = + ( 0)
http://www.manabino-academ.com = () = ( ) = ( ) ( ) = = ( ) = = ( ) = + = + = + + = + + ( ) (4) = + ( 0) = ( ) + = + = 0 = 0 + = < = + = + ( ) = + \= = + = + ( < ) = + () = (0 4) () = + 5 () = + + ( ) (4) = + ( 0)
http://www.manabino-academ.com.4 b = f(a) a = f (b) 4 f() = a + + b f () f() = 9, f () = a, b f() f () = f( ) = (i) f() = 9 (ii) f( ) = f() = a + + b = 9 a + = 9b + 6 a 9b = 5 f( ) = a + ( ) + b = a + = b 4 a + b = 5, a = 4, b =
http://www.manabino-academ.com.5 = f() = = f () f() = f () = f() = f () = = = f() = f () = f() = 5 f() = + () = f() = f () () f() = f () () 0 = + ( ) = 0 + = = = ( 0), (), =, = =
http://www.manabino-academ.com 4 f() = f () f() =, f () = = = 0 ( )( + ) = 0 0 = 5 f() = ( ) f () f()
http://www.manabino-academ.com 5.6 f() g() ( i ) ( ii ) f() = g() 6 = a + () () = + c a, b, c b + () = a + a( + ) a = + = a + + + a a + = 0 = a a + \= 0 () \= a ( + ) = a + = a ( a) = \= a = a = a = + c b + a = + c b + a =, b =, c = ( ) + + a = + c b +
http://www.manabino-academ.com 6 4 4. t = g(t) t t = f() = g(f()) f g g(f()) (g f)() (f g)() \= (g f)() f, g, (f g)() = f(g()), (g f)() = g(f()) (h (g f))() = ((h g) f)() 4 f() = +, g() = + () (f g)() () (g f)() () (f f)() (4) (g g)() () (f g)() = f(g()) = ( + ) + = + + = + 5 () (g f)() = g(f()) = ( + ) + = (4 + + 9) + = 4 8 () (f f)() = f(f()) = ( + ) + = 4 + 6 + = 4 + 9 (4) (g g)() = g(g()) = ( + ) + = ( 4 + ) + = 4 + 4 f() =, g() =, h() = ( ) () (f g)() () (g h)() () ((g f) h)() (4) (g (f h))()
http://www.manabino-academ.com 7 4. = + = = = + (f() = + ) ( f () = ) + = f(f ()) f() f () f(f ()) = f (f()) = 4 f() = +, g() = 6 h(f()) = g() h() = + = = (= f ()) f() h(f()) = g() h(f(f ())) = g(f ()) 4 h() = 6 = 4 f() = +, g() = () g(f()) () h(g()) = f() h()