8 ) ) [ ] [ ) 8 5 5 II III A B ),,, 5, 6 II III A B ) ),,, 7, 8 II III A B ) [ ]),,, 5, 7 II III A B ) [ ] ) ) 7, 8, 9 II A B 9 ) ) 5, 7, 9 II B 9 ) A, ) B 6, ) l ) P, ) l A C ) ) C l l ) π < θ < π sin θ + cos θ = sin θ cos θ ) 6 8 = 6 = 6 = ) 6 = ) ) = ) = 8 5 6 ) p = 8 + p 7. < log <.
n y = e x P n n, e n ) x x a n x Q n n, ) R n a n, ) ) a n n ) P n Q n R n n ) y = e x x = x = a n x P Q R P Q R P n Q n R n S n lim S n n y = tan x x π ) x = π x S ) S ) fx) = tan x x ) S x 5 OABC OA = OB = OC = AB = BC = CA = OB P AP OB OA OB OC a b c ) OP b ) APC ) OAC Q PQ OAC OQ a c OAC O A C 6 log x x ) < x < π logcos x) + x < ) π π log + 8 < logcos x) dx < π 6
7 C : y = x P, ) l l y = Q Q C l m ) l ) m ) l m C S 8 {a n } n S n S n = a n + n ) n a n a n ) n b n = a n+ a n b n n ) a n n 9 O A, ) B, ) C, ) D, ) P AB POA = θ θ 5 ) ) PC θ ) PA + PC PD
) C Qa, b) AQ = PQ a + b = A, ) B 6, ) a ) + b + ) = a ) + b + ) l + 6 = l AQ b + a = a + b = 5 a = b = 7 ) AQ = + 7 ) + = 7 9 x ) + y + 7 ) = 7 9 ) C Rx, y ) AR Q + x =, + y = 7 x =, y = x = y = ), y + = x ) x y 58 =
5 ) π < θ < π sin θ cos θ = sin θ π ) < sin θ + cos θ) + sin θ cos θ) = sin θ + cos θ = + sin θ cos θ) = sin θ cos θ) = 7 7 sin θ cos θ = ) 5 a a = a a = ) ) = 8 ) a = 6 p = 8 + 7 = ) 7 + 6 + = a7 6 + a + = ) k a 6 k k= p = a 6 a 5 a ) a a ) a ) p = a 6 a 5 + a a ) + a a ) + + a a) + a )a 5 < p < a 6 < 5 < p < < p < + log < log p < log. = +. < log p <. =.88 < log p < < p < p a + b = a + b)a ab + b ) a 5 + b 5 = a + b)a a b + a b ab + b ) a n+ + b n+ = a + b) n k= ) k a n k b k mod 7) ) 7 ) 7 mod 7) 8 + mod 7)
6 ) y = e x y = e x y = e x P n n, e n ) y e n = e n x n) y = e n x n ) x x a n a n = n + ) ) Q n R n = a n n = P n Q n = e n e n P n Q n R n = Q nr n P n Q n = e n = e`n O y Q n P n n a n R n x ) ) S n = n+ e x dx [ ] n+ = e x n k= e k e e n e = e n + e e n e ) lim n S n = e e ) = e ee ) ) S = tan x = [ ] π log cos x ) f x) = tan x x) = cos x = tan x ) ) [ V = π tan x dx = = log = log tan x x ] π = π π )
7 5 ) θ = AOB cos θ = OA + OB AB OA OB = + = 7 8 P OP = OA cos θ C B = 7 8 = 7 A b OP A O O θ P B OP = OP b = 7 b = 7 b 8 ) ) P AP = OA sin θ = cos θ ) 7 5 = = 8 C 5 ABP CBP CP = AP = ) ) CA M PM = 5 = M 5 A APC = CA PM = = ) a = b = c = AOB = BOC = COA = θ a b = b c = c a = cos θ = 7 8 = 7 Q OM OM e e = c + a c + a = c + a c + c a + a = OQ = OP e) e = 5 = 7 7 + 7 8 c + a + 7 + = c + a 5 { } 7 b c + a) c + a) = 7 8 b c + a b) c + a) ) c + a) = 9 c + a)
8 6 ) < x < π tan x > x tan t dt > tan x x > x tan t t) dx > logcos x) x > logcos x) + x < ) ) logcos x) < x logcos x) dx < = x ) dx [ 6 x ] π [ ] π logcos x) dx = x logcos x) = π log + = π 6 x tan x dx x{logcos x)} dx < x < π tan x > x x tan x dx > x dx = [ ] π x = π 8 π π log + 8 < logcos x) dx < π 6
9 7 ) y = x y = x C P, ) l y = x ) y = x ) ) l y = Q, C y R a, a P ) a ) a y a = ax a) y = ax a Q R O x Q, ) = a a a a = l m a )a + ) = a a = y = x ) S S = = = [ { x x x + ) dx + )} dx + x + ) ] + x ) dx [ x ) {x x )} dx ] = 5 96 C l m 9 ). C P R l m Q x P R x. C PR S C l m S S x x ) S = S, S = { )} = 5 6 8 http://kumamoto.s.xrea.com/nyusi/qdai bun 9.pdf
8 ) n S n = a n + n S n = a n + n S n S n = a n a n + S n S n = a n a n = a n a n + a n = a n` ) ) n a n+ = a n+ a n+ = a n a n+ a n+ = a n+ a n ) b n+ = b n S = a +, S = a, a = a a =, a = {b n } b = a a = ) ) ) b n = n = n a n+ = a n, b n = a n+ a n a n+ a n = b n + a n = n +
9 ) POA = θ PCA = θ APC = 9 PC = CA cos θ = cos θ ) ) PA = CA sin θ = sin θ y B P POB = 9 θ PDB = POB = 5 θ DPB = 9 PD = DB cos 5 θ) = cos 5 θ) C θ θ O 5 θ D A x PA + PC = sin θ + cos θ = cos 5 θ), PA + PC PD = cos 5 θ) cos 5 θ) = ) cos 5 θ) θ 5 cos 5 θ) PA + PC PD )