4 4 5 4 I II III A B C, 5 7 I II A B,, 8, 9 I II A B O A,, Bb, b, Cc, c, c b c b b c c c OA BC P BC OP BC P AP BC n f n x xn e x! e n! n f n x f n x f n x f k x k 4 e > f n x dx k k! fx sin x cos x tan x + x π x π fx y fx x x π x π
4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx gx fx x x gx x ft dt x 7 ft dt + 7, gt dt x + x x + fx gx y fx 4, f4 l l y gx
8 OAB OA a OB b AOB θ a b < θ < 9 B OA A A AB OB B B OA A A A B OB B OA B, OA B,, OA n B n OA n B n OAB A n B n a b θ A n B n OA k B k S k a b θ n S + S + + S n 9 a > C : y x Pa, a C l P l l l C P Q Q a C l S S a S a
4 OA,, OB b, b, OB OA b + b AOB OA OB OA OB cos b b b b > b 4 OC c, c, c OC OA c + c + c AOC OA OC OA OC cos c c BOC OB OC OB OC cos c + c c + c c 4 4 c OA,, BC,,,,,, c > c OA BC + + OA BC
5 BC P t OP OB + t BC OP BC OP BC OB + t BC BC OB BC + t BC 5 OBC OB BC BO BC BO BC cos, BC 5 t OP OB + BC,, +,,, P,, AP,,,,, AP BC + +,, AP BC
f nx nxn e x + x n e x n! xn e x n! xn e x f n` x f n x n! f x e x f x e x f x f kx f x + k f n x f x + f kx k {f k x f k x} k f x + {f x f n x} xne`x f n x n! f kx k f n x dx k [ f k x k f kx dx f k + k ] f k k f n e n! f n n f f n x dx k e k! + e k k! + 4 < x f n x > f n x dx > e k! + > e > k! k k
7 fx f x cos x sin x cos x + 4 cos x cos x 4 cos4 x cos x cos x + cos x cos x fx x π π π 4 f x + fx π π + π x π 4 π x π π f fx π x fx, x π fx fx F x sin x + log cos x + x S S π [ F x F π 4 + log fx dx + ] π + 5 π + log π [ + F x fx dx ] π π + F F + π + 4 4 + log + π 9
8 4 A a c b d A a de a c b d a d d c b a A a da A{A a de} a b d b c d c a ad bc ad bce ad bc A a da ad bce O A n O deta n det O det A ad + bc det A n A a da n A n a d n A ad bc A O a d a d ad bc a d A O n A n O a d, ad bc a d bc a d b, c, a d b, c, 4,,, 4, a d b, c, a d 4 b, c 4, 4 a d 5 b, c 5, 5 a d b, c, 8 4
9 5 a n + S n a + n S S a a + a a + a a + a + 9 a a a a n+ + S n+ S n+ S n + a n+ a n+ + S n + a n+ a n+ + a n+ + 9 S n + a n+ a n+ S n {a n } S n S a n + S n S a n a n+ S n S n n A a n+ + S n i n S n A ii n k A S k+ S k + a k+ S k + + S k k + + k k + + k k + n k + A i ii A a n+ + S n+, a n + S n a n+ a n + a n+ a n S n+ S n a n+ a n+ + a n a n+ a n a n > a n+ a n + {a n } a n n S n n
x x > < x < x x x + 4 < xy < x < y x + y y + x O x y x + x x + y y + < x < x x + y x + x + x x + + + x x + + x x y + + x > x > x + x x x x x x x + x + +
7 a ft dt b ft dt fx a x b 7 x + 7 a a ft dt t b 7 t + 7 dt [ a t b ] 4 t + 7t a b 4 + 7 b ft dt [ a t b 4 t + 7t a t b 7 t + 7 dt ] a + b 4 + 7 a b 8 fx x 4x + 7 x gx x x gt dt x + x x + gt dt x gx + x x + x gx gx px + qx + r x gt dt x px + qx + r + x x + x p + x + p + q x + q + r + x r x r r x px + qx + r p + x + p + q x + q + r + p p +, q p + q, r q + r + p q gx x + x
x gx x x g x gt dt x + x x + g gx + x g x gx x + 4x x g x x gx x g x x gx g x a g a lim x a g x lim x a x + a + a g x x + gx x + x f4 4 4 4 + 7 7 f x x 4 f 4 4 l y 7 4x 4 y 4x 9 hx 4x 9 gx hx x +x 4x 9 x +x 8 x+4x y gx y hx x x 4, 4 x gx hx S S 4 {gx hx} dx 4 x + 4x dx { 4}
8 OA n B n OAB A O A A n B n //AB A OA n B n OAB θ OA n B n OAB O B B B OA n B n OAB A n B n A n B n OA n OB n cos θ OA n OA n OB cos θ OA b cos θ a a b θ A n B n A n B n cos 4 S n An B n S n A n B n S OAB sin S + S + + S n S + S + + S n { n } { n }
4 9 y x y x C Pa, a l a l l a l y a x a a l C y x a x a a P Q x x a a Q a a, a a a x a x + a + a y y a + a a + a a a x a l : y a x a + a C : y x S a { S } dx a a { a a x a + a x x + a + a x a a a } dx a + a a > a > a + a a a a a a S 4 a a