6 ( ) 6 5 ( ) 4 I II III A B C ( ) ( ), 5 7 I II III A B C ( ) () x π y π sin x sin y =, cos x + cos y = () b c + b + c = + b + = b c c () 4 5 6 n ( ) ( ) ( ) n ( ) n m n + m = 555 n OAB P k m n k PO + m PA + n PB = () k = 4 m = n = POA POB PAB () k P m n m + n = P () P k m n m + n = P D D OAB
n = n + { n } k k, 4, 5, 6 7, 8, 9, 4 k S k () S k () = S k () = 9 S k = S k+ k 4 f(x) f(x) = cos x f(t) sin x dt () f(x) () f(x) sin x dx = π () () ( ) ( ) ( ) x π f(x) ( ) f(x) dx 5 ABCDEF DE P AP BF Q () AP AB AF () AQ : QP () AB = BPQ
6 n = n + { n } k k, 4, 5, 6 7, 8, 9, 4 k S k () S k () S k () S k = S k+ k 7 y = log x C e ( (), ) C () () C x () C y = x e C y = x x e
4 () sin y = sin x, cos y = cos x sin y + cos y = ( sin x ) + ( cos x ) = ( sin x cos x = sin x π ) = 6 x π x = π sin y =, cos y = y π y = π () ( + b + c) =, b + bc + c bc = f(x) = (x )(x b)(x c) f(x) = b c f() = ( )( b)( c) = ( + b + c) + b + bc + c bc = f(x) = b c
5 ()( ) 4 5 6 6P = ( ) 5P = ( ) = ( ) ( ) A = {, 5} B = {, 4} C = {, } A b B c C n b c 4 bc, bc, cb, cb b c 4 = ( )
6 () AB n : m Q m PA + n PB = (m + n) PQ O k PO + m PA + n PB = ( ) m+n P k A n Q m B k PO + (m + n) PQ = ( ) P OQ m + n : k S = OAB k PAB = k + (m + n) S, m + n POB = k + (m + n) OBQ m + n = k + (m + n) m + n POA = k + (m + n) OAQ m + n = k + (m + n) m m + n S = n m + n S = m k + (m + n) S, n k + (m + n) S ( ) PAB : POB : POA = k : m : n POA : POB : PAB = n : m : k = : : 4 () m + n = ( ) k OP + ( OQ OP) = O OP = OQ k + OA OB : k A B m n P A B A A P B () k = A B OA OB : k m n D OA B D OAB ( ) = 9 4 6 n Q k m B
7 () k { n } k(k )+ k(k+) k(k )+ = { k(k ) + } + = k + k + k(k+) = k(k + ) + = k k + S k = k{( k + k + ) + ( k k + )} = k + ( )k () () = S k = k + k S k+ S k = { (k + ) + (k + )} ( k + k) = {7 k(k + )} S < S < < S 8 > S 9 > S > S k () S k k = k + k k 8 + = 47 = k + () () = 9 S k = k + 9k S k+ S k = { (k + ) + 9(k + )} ( k + 9k) = (k 5)(k + 6) S k+ + S k = { (k + ) + 9(k + )} + ( k + 9k) = k k + 79k + 9 = (k 9)(k + )(k + ) S k = S k+ k k = 5, 9 S k = k(9 k ) k 9 S k > k S k+ < S 9 = 9, S = 9 S k+ + S k k 9
8 4 () f(x) = cos x sin x f(t) dx k = f(t) dt f(x) = cos x k sin x k = ( cos x k sin x) dx [ = sin x + k cos x ] π = k > k = k k k = + f(x) = cos x + sin x () () f(x) sin x dx = = π + = π ( sin x cos x { sin x ) + sin x } ( cos x) + dx = dx = π + ()( ) () () f(x) = sin x + cos x cos α = sin α = α ( < α < π) 5 5 f(x) = 5 sin(x α) f() = f(α + π ) = 5 ( ) ( ) f(x) dx = α 5 sin(x α)dx + 5 sin(x α)dx α = [ ] α 5 cos(x α) [ ] π 5 cos(x α) = 5 ( cos α) 5 ( cos α ) = 5 α
9 5 () AD = AB + AF AE = AB + AF AP = ( AD + AE) = AB + 4 C AF D () () AP = 7 AB + 4 AF 7 AQ = AB + 4 AF AP = 7 AQ 7 AQ : QP = : 7 = : 5 B A Q P F E () ABF = sin = BQ : QF = 4 : () ABQ = 4 4 + ABF = 4 7 4 4 = BPQ = 5 ABQ = 5 7 = 5 4 7
6 () k { n } k(k )+ k(k+) k(k )+ = { k(k ) + } + = k + k + k(k+) = k(k + ) + = k k + S k = k{( k + k + ) + ( k k + )} () () = k + k S k+ S k = { (k + ) + (k + )} ( k + k) = {7 k(k + )} S < S < < S 8 > S 9 > S > S k () S k k = k + k k 8 + = 47 () () = k + S k+ + S k = { (k + ) + (k + )} + ( k + k) = k k + 49k + = (k 4)(k + 5)(k + ) S k = S k+ k k = 4 S k = k( k ) k 4 S k > k 5 S k+ < S 4 = 4 5, S 5 = 5 4 S k+ + S k k 4
7 () y = log x y = ( ) x t, log t t y log t = t (x t) y = x t + log t (, ) log t = y = x e + t = e () y = log x x = x = e x S S = e log x = [ x(log x ) ] e = (e e + ) i) < < {e e ( )} S = e (e e + ) ) y O e ( ) e x =e ( + ii) { ( e + )} S ( =e ) (e e + ) y O e x = e
() C y = x x u e log u = u e y = x e y = x e u = u e u = e = y y = x e O e C x S e x e S = e dx log x dx [ ] x e [ = x(log x ) 6e = e ] e