8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,, 4) D(,, 4) () BAC = θ cos θ ABC () AB AC () D A B C E DE (4) ABCD 4 f(x) = e x g(x) = e x () f(x) g(x) x () h(x) = f(x) g(x) h(x) () y = g(x) y = e y
5 {a n } a =, a n+ =.5 a n (n =,,, ) () a n () a n n log =. log =.477 log 7 =.845 6 C : y = (x a)(x 4)(x b) a b a < 4 < b () C x a + b () a > C x y a b 7 {a n } a =, a n+ = a n + (n =,, ) () < a n < (n =,, ) () cos b n = a n < b n < π b n () lim a n n 8 { x x + a } x + a dx = a a
() ( + x) n = n nc k x k k= ( ) x = n = n nc k k= n nc k = n k= n = 7 n = 7 n = 7 () ( ) x = n = 7 7 = 7 7C k k k= 7 = + 7 C + 7 = 5 + 9 k= k= 7C k k 7C k k 7 9 5
4 () y = x x y = x C (a, a a) y (a a) = (a )(x a) y = (a )x a A(, 6) 6 = (a ) a a =, y = 5x 6, y = x () C P(t, t t) AP Q(x, y) t = x x = + t, y = 6 + t t y = 6 + (x ) (x ) = x 7x + Q y = x 7x + () y = x 7x + y = x y = 5x 6 y y y=x 7x+ x 4x + = (x ) = (, ) y O x y=5x 6 x x + 8 = (x ) = y= x (, ) S S = = = {(x 7x + ) ( x)} dx + (x ) dx + [ (x ) ] + {(x 7x + ) (5x 6)} dx (x ) dx [ (x ) ] = 4 http://kumamoto.s.xrea.com/kyusuu/kyukou/kyukou jou 4.pdf
5 () AB = (,, ) AC = (,, 4) cos θ = ABC = AB = + + = 6, AC = ( ) + + ( 4) = 6, AB AC = ( ) + + ( 4) = 6 AB AC AB AC sin θ = cos θ = = 6 6 6 = ( ) = = ABC = AB AC sin θ = 6 6 AB AC ( AB AC) = 6 4 6 = () n = (x, y, z) AB n = AC n = x + y + z =, x + y z = x : y : z = : : (,, ) () AD = (,, 4) n = (,, ) α cos α = AD n AD n DE = AD cos α = = + 4 AD + + (4) () () ABC DE = = = AD ( ) AB AC = (,, ) (,, 4) = ( 6, 6, 6) ABC = AB AC = ( AB AC) AD = ( 6, 6, 6) (,, 4) = 8 ABCD V V = 6 ( AB AC) AD = 6 8 = http://kumamoto.s.xrea.com/nyusi/qdai ri 4.pdf 4
6 x 4 () f(x) g(x) e x e x e > x x(x ) x () h(x) = f(x)g(x) = e x e x = e x +x ( x + x = x + ) 4 6 h(x) x = 4 6 () y = e x x = log y e` y e y = e e [ ] e π log y dy = π y(log y ) O x = π(e + ) V V = π x(e e x )dx [ e = π x ex = π(e + ) ] y y = e x a x b f(x) y = f(x) x x = a x = b y V V = π b a xf(x) dx
7 5 () a n+ =.5 a n a n+ =.5(a n ) {a n } a =.5 a n =.5 n a n =.5 n` () a n.5 n.5 n (n ) log.5 log log.5 = log = log + log 7 (log + ) =.477 +.845. =. n log log.5 + = 5. n 6
8 6 () C C C P P x P (4, ) y = (x a)(x 4)(x b) y = 6x (a + b + 4) x = 4 y = 6 4 (a + b + 4) = a + b = 8 () () y (x a)(x 4)(x b) =x (a + b + 4)x + (ab + 4a + 4b)x 4ab =x x + (ab + )x 4ab O a 4 b x 4 (x a)(x 4)(x b) dx = 4 (x a)(x 4)(x b) dx = = 4 {x x + (ab + )x 4ab} dx [ 4 x4 4x + (ab + )x 4abx = 4 4 4 + 8(ab + ) 6ab = 8ab + 64 ] 4 8ab + 64 = ab = 8 () a b t 8t + 8 = a < b a = 4, b = 4 +
9 7 () < a n < (n =,, ) ( ) n = a = ( ) n = k ( ) a k+ = a k + > a k+ = a k + = a k + a k + > n = k + ( ), n ( ) ( () () a n cos b n = a n b n < b n < π ) a n = cos b n a n+ = a n + cos b n+ = cos b n + = cos b n+ = cos b n a = cos b = a = π b n+ = b n 4 cos b n = cos b n b = π 4 {b n } 4 ( ) n` (n =,,, ) b n = π 4 () () lim b n = n lim a n = lim cos b n = cos = n n a n+ = a n + a n + < a n a n < ( ) n a lim a n = n a n < a n+ a n = a n + a n = ( a n)( + a n ) > an + + a n {a n } α lim a n+ = lim an + n n α = α + α = http://kumamoto.s.xrea.com/kyusuu/nagasaki/nagasaki 8.pdf 8
8 ( ) x x + a dx = x a dx + a x x + a dx = = ( ) x a dx = (x ) + a dx x + a dx = [ 4 x ax ( ) (i) a < ] = a x + a dx = a + a ( ) x + a dx = (x + a ) dx [ = x + (a )x ( ) x + a dx, ] = a ( ) ( ) a = a + a a = a < a = (ii) a t = a ( t ) x + a dx = = t x t dx (x t ) dx + [ x = t x = 4 t t +, ] t t (x t ) dx [ x + t x a + a = ( a) = t 4 ( 4 ( ) t t + ) = t 4 ] t
t 4 8t + 6t = f(t) = t 4 8t + 6t < t < f (t) = t 4t + t = t(t ) > f(t) < t < f() = < f(t) = t ( t ) (iii) a > x + a dx = (x + a ) dx [ x = + (a )x ] = a ( ) ( a ) = a + a a a + 7 = a > a = 6 + 5 (i) (iii) a a =, 6 + 5