2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a
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- あかり かやぬま
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1 009 I II III 4, 5, α β α β l 0 l l l l γ ) γ αβ ) α β. n n cos k n n π sin k n π k k 3. a 0, a,..., a n α a 0 + a x + a x + + a n x n 0 ᾱ 4. [a, b] f y fx) y x 5. ) Arcsin 4) Arccos ) ) Arcsin ) 3) Arccos 3 5) Arctan 3 6) Arctan 3 ) 6. n ) tan x nπ π/, nπ + π/) f n x) f n x) fn x) Arctan x ) sin x [nπ π/, nπ + π/] g n x) cos x [nπ, n + )π] h n x) g n x) x) h n x) h x) Arcsin x g n n
2 7. ) cos Arcsin x) ) tan Arcsin x) < x < ) 3) sin Arctan x) 4) sin Arctan x) 8. Arctan tan x ) π 4 Arctancos x) ) ) 9. ) cosh x sinh x ) tanh x cosh x 3) sinhx + y) sinh x cosh y + cosh x sinh y 4) coshx + y) cosh x cosh y + sinh x sinh y 5) tanhx + y) tanh x + tanh y + tanh x tanh y 0. ) cosh x, sinh x, tanh x cosh x x 0 x 0 ) ). ) tanh x ) tan x) x 3) Arcsincos x) 4) Arctan x + x
3 009 I II III 4, 5, ,, α β 0, β, αβ β β β 0,, α 0, β, αβ 0,, β 0, α, αβ α 0 αβ β γ : 0α 0βαβ) 0β 0ααβ) γ αβ 0, β, αβ 0, α, αβ αβ 0,, α α, 0,, β β α β [0, ] / / α α rcos θ + i sin θ) α r θ
4 000 n cos k n n π + i sin k n π k k e k n πi cos k n π + i sin k n π n k cos sin e k n πi e πi) k n cos kn π + i sin kn ) π ζ e πi/n n n e k n πi ζ k ζ + ζ + + ζ n ζ ζn ζ k ζ n k e n πi) n e n n πi e πi ζ ζn ζ ζ ζ 0 n k e k n πi 0 0 n cos k n π k n k sin k n π 0 e kπi/n coskπ/n) + i sinkπ/n) kπ/n k k n n 0 0 e iθ e iφ e iθ+φ) sin cos e iθ+φ) cosθ + φ) + i sinθ + φ) cos θ cos φ sin θ sin φ + i sin θ cos φ + i cos θ sin φ cos θ + i sin θ)cos φ + i sin φ) e iθ e iφ
5 3 e πi/5 e 4πi/5 e 6πi/5 O e 0πi/5 e 8πi/5 : coskπ/n) + i sinkπ/n) n 3 α a 0 + a α + a α + + a n α n a 0 + a α + a α + + a n α n a 0 + a α + a α + + a n α n a 0 + a ᾱ + a ᾱ + + a n ᾱ n a 0 + a ᾱ + a ᾱ + + a n ᾱ n a 0 + a ᾱ + a ᾱ + + a n ᾱ n 0 ᾱ x 3x i 0 + i i 4
6 4 M m [m, M] [m, M] y fx) y x fx) m x fx) M x fa ) fa ) m, a < a ) fb ) fb ) M, b < b ) CASE : a < a < b < b fa ) m, fb ) M [m, M] y fx) y x [a, b ] a < c < a c fc) m fx) m x fc) > m m < y 0 < fc) y 0 y 0 a < c < c fc ) y 0 c c < c < a fc ) y 0 c [a, b ] fx) y 0 x 3 M y 0 m a a b b 3: CASE y fx) CASE : a < b < a < b m < y 0 < M y 0 fx) y 0 x a, b ) b, a ) a, b ) CASE 3 : b < a < a < b a < c < a c fx) fc) x [b, a ] [a, b ] fx) fc) x
7 5 CASE 4 : a < b < b < a CASE 3 m M CASE 5 : b < a < b < a CASE m M CASE 6 : b < b < a < a CASE m M CASE 5 ) π 6, ) π, 3) π 6, 4) 3 4 π, 5) π 6, 6) π 3 ) Arcsin sin θ π θ π θ Arcsin π 6 )
8 6 6 ) y 0 tan x y 0 x tan x 0 y 0 x 0 x x 0 + mπ m Arctan y 0 tan x y 0 x π/ < x < π/ tan x y 0 x Arctan y 0 x Arctan y 0 + mπ m f n x) nπ π/, nπ + π/) nπ π < f n y 0 ) < nπ + π fn y 0 ) x n x 0 + nπ Arctan y 0 + nπ y 0 fn x) Arctan x + nπ ) y 0 y 0 sin x y 0 x sin x 0 y 0, π/ x 0 π/ x 0 x mπ + ) m x 0 m cos x sin x + π/) cos x y 0 sin x + π ) y 0 cos x y 0 x x 0 x mπ + ) m x 0 π m π + ) m x 0 m sin x y 0 x π/ x π/ Arcsin y 0 x x x mπ + ) m Arcsin y 0, x m + ) m Arcsin y 0 m Arcsin y 0 nπ π g n y 0 ) nπ + π, nπ h n y 0 ) n + )π n gn y 0 ) x m n h n y 0 ) x m n + gn y 0 ) nπ + ) n Arcsin y 0, h n y 0 ) n + π + ) n+ Arcsin y 0 y 0 [, ] gn x) ) n Arcsin x + nπ, h n x) ) n+ Arcsin x + n + π
9 7 h 0 x) Arccos x Arccos x Arcsin x + π y x 80 4 y f f π Arctan x f 0 f O x f Arcsin x g 0 g g g y O g x h h y O h 0 Arccos x x h 4: f n, gn, h n 7 ) sinarcsin x) x cos θ sin θ cos θ π/ θ π/ 0 cos θ sin θ π θ π
10 8 π/ Arcsin x π θ Arcsin x cos Arcsin x) sin Arcsin x) x ) ) tan θ sin θ cos θ sin θ sin θ π θ π θ Arcsin x sin Arcsin x) x tan Arcsin x) sin Arcsin x) x 3) tan Arctan x) x sin θ tan θ π/ θ π/ cos θ 0 cos θ cos θ cos θ sin θ + cos θ cos tan θ + θ sin θ tan θ cos θ θ Arctan x sin Arctan x) tan θ tan θ + tan Arctan x) tan Arctan x) + x x + 4) sin Arctan x) sin Arctan x) cos Arctan x) sin Arctan x) 3) cos Arctan x) 3) cos θ θ Arctan x + tan θ cos Arctan x) π < θ < π x + x sin Arctan x) x + x + x x +
11 9 8 ) tan θ θ tan Arctan y) y tan θ) tan θ tan Arctan tan x )) tan x tanθ + φ) π ) tan 4 Arctan cos x) tan θ + tan φ tan θ)tan φ) tan π 4 tan Arctan cos x)) + ) tan π 4 tan Arctan cos x))) cos x + cos x sin x cos x tan x tan π Arctantan x) π Arctan cos x) + nπ 4 n n x 0 0 π Arctan + nπ 4 Arctan π/4 n 0 ) Arctantan x) + Arctancos x) π Arctan x) + x
12 0 Arctantan x) ) tan + tan x ) tan x x) + tan 4 x cos x cos 4 x sin x cos 4 x + sin 4 x cos 3 x sin x cos x cos 4 x + sin 4 x Arctancos x)) + cos x cos x) sin sin x) x + cos x 4 sin x cos x 4 sin x cos x + cos x sin x) 4 sin x cos x 4 sin x cos x + cos 4 x 4 cos x sin x + sin 4 x sin x cos x cos 4 x + sin 4 x Arctantan x) + Arctancos x) ) Arctantan x) ) + Arctancos x)) 0 Arctantan x) + Arctancos x) x 0 Arctantan 0) + Arctan cos 0) ) Arctan 0 + Arctan 0 + π 4 π ) cosh x sinh x e cosh x sinh x + e x ) e x e x ) x ex + + e x cosh x sinh x ) cosh x sinh x sinh x cosh x 0 ex + e x 4 x 0 cosh 0 sinh 0 0
13 ) tanh x ) tanh x sinh x cosh x cosh x sinh x cosh x ) cosh x 3) sinh x cosh y + cosh x sinh y ex e x e y + e y + ex + e x ex e y + e x e y e x e y e x e y 4 ex e y e x e y ex+y e x+y) e y e y + ex e y e x e y + e x e t + e x e y 4 sinhx + y) 4) 3) cosh x cosh y + sinh x sinh y ex + e x e y + e y + ex e x ex e y + e x e y + e x e y + e x e y 4 ex e y + e x e y ex+y) + e x+y) e y e y + ex e y e x e y e x e y + e x e y 4 coshx + y) 5) 3) tanh x + tanh y sinh x cosh x + sinh y cosh y sinh x cosh y + sinh y cosh x cosh x cosh y 4) sinhx + y) cosh x cosh y + tanh x tanh y + sinh x sinh y cosh x cosh y cosh x cosh y + sinh x sinh y coshx + y) cosh x cosh y cosh x cosh y tanh x + tanh y tanhx + y) + tanh x tanh y
14 cosh x : ex + e x, sinh x : ex e x, tanh x : sinh x cosh x ex e x e x + e x cosh sinh tanh cosh x e x y e x sinh x tanh x O x tanh x sinh x e x 5: cos θ + sin θ cos θ, sin θ) x + y ) cosh t sinh t
15 3 cosh t, sinh t) x y sinh t R R cosh t cosh t, sinh t) x y x > 0 9 ) 5) θ 0, 0) cos θ, sin θ) x t t 0, 0) cosh t, sinh t) x x y x ±π/4 cosh t, sinh t) t cos t, sinh t) x y x > 0 x x y x y y sinh t sin t x + y t cos t O x O cosh t t θ x cos θ, sin θ) x + y x. ABC BC, CA, AB a, b, c sin A a sin B b sin C c
16 4 sin A sinh a sin B sinh b sin C sinh c tanh t 5) cos t eit + e it, sin t eit e it i cosh t et + e t, sinh t et e t 0 ) y cosh x x y cosh x ex + e x ex ) + e x e x ) e x y + 0 e x y ± y x log y ± ) y x y ± y y cosh x y y + y y 0 y y y ) y ) y + 0 y y
17 5 x log y + ) y 0, x log y ) y 0 x y x cosh x x 0) cosh x log x + ) x [, ) [0, ) cosh x x 0) cosh x log x ) x [, ), 0] y sinh x y sinh x ex e x ex ) e x e x ) ye x 0 e x y ± y + e x 0 y y x log y + ) y + x sinh x sinh x log x + ) x + y tanh x x y tanh x ex e x e x + e x ex ) e x ) +
18 6 e x 0 y) e x ) + y e x + y y tanh x, ) + y x log y log + y y x tanh x tanh x log + x x, ) ) ) cosh x x 0) cosh x cosh x ) log x + )) x + x ) x x + x + x x x + x x + x x + x x x y cosh x 9) cosh x ) cosh y sinh y cosh y sinh y y 0 sinh y 0 sinh y cosh y x cosh x ) x cosh x x 0) ) cosh x ) log x )) x x ) x x x x x x x x x x x x x
19 7 y cosh x cosh x ) cosh y sinh y cosh y sinh y y 0 sinh y 0 sinh y cosh y x cosh x ) x sinh x ) sinh x ) log x + )) x + x + ) x + x + x + + x x + x + x + x + + x x + x + x + x + y sinh x cosh y > 0 sinh x ) sinh y cosh y cosh y cosh y sinh y sinh y + x + sinh x ) x + tanh x ) tanh x ) log + x ) ) + x x x x + x +x x x) ) + x) x) x y tanh x tanh x ) tanh y cosh y
20 8 9 ) tanh y cosh y tanh x ) tanh y x ) tanh x tanh x ) sinh x cosh x sinh x cosh x cosh x cosh x tanh x tanh x cosh x tanh x cosh x sinh x cosh 3 x sinh x fx) log fx) ) f x) fx) f x) fx)log fx) ) sinh x log cosh x log sinh x) log cosh x) cosh x sinh x sinh x cosh x cosh x sinh x ) sinh x tanh x cosh x cosh x sinh x cosh 3 x sinh x
21 9 ) tan x) x ) e x logtan x)) x logtan x)) e x logtan x) ) logtan x) + tan x) x x sin x logtan x) + x / ) cos x tan x) x tan x 3) Arcsincos x)) cos x cos x sin x sin x 4) Arctan ) x + x + x +x + x +x x ) x + x ) x + x) x) + x + x)
2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta
009 IA 5 I, 3, 4, 5, 6, 7 6 3. () Arcsin ( (4) Arccos ) 3 () Arcsin( ) (3) Arccos (5) Arctan (6) Arctan ( 3 ) 3. n () tan x (nπ π/, nπ + π/) f n (x) f n (x) fn (x) Arctan x () sin x [nπ π/, nπ +π/] g n
di-problem.dvi
005/05/05 by. I : : : : : : : : : : : : : : : : : : : : : : : : :. II : : : : : : : : : : : : : : : : : : : : : : : : : 3 3. III : : : : : : : : : : : : : : : : : : : : : : : : 4 4. : : : : : : : : : :
. sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y = e x, y = e x 6 sinhx) coshx) 4 y-axis x-axis : y = cosh x, y = s
. 00 3 9 [] sinh x = ex e x, cosh x = ex + e x ) sinh cosh 4 hyperbolic) hyperbola) = 3 cosh x cosh x) = e x + e x = cosh x ) . sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y =
1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................
1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ
1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c
(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)
2017 12 9 4 1 30 4 10 3 1 30 3 30 2 1 30 2 50 1 1 30 2 10 (1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) (1) i 23 c 23 0 1 2 3 4 5 6 7 8 9 a b d e f g h i (2) 23 23 (3) 23 ( 23 ) 23 x 1 x 2 23 x
211 [email protected] 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X
4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0
x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
arctan 1 arctan arctan arctan π = = ( ) π = 4 = π = π = π = =
arctan arctan arctan arctan 2 2000 π = 3 + 8 = 3.25 ( ) 2 8 650 π = 4 = 3.6049 9 550 π = 3 3 30 π = 3.622 264 π = 3.459 3 + 0 7 = 3.4085 < π < 3 + 7 = 3.4286 380 π = 3 + 77 250 = 3.46 5 3.45926 < π < 3.45927
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, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f
,,,,.,,,. R f : R R R a R, f(a + ) f(a) lim 0 (), df dx (a) f (a), f(x) x a, f (a), f(x) x a ( ). y f(a + ) y f(x) f(a+) f(a) f(a + ) f(a) f(a) x a 0 a a + x 0 a a + x y y f(x) 0 : 0, f(a+) f(a)., f(x)
S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt
S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............
S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
( ) sin 1 x, cos 1 x, tan 1 x sin x, cos x, tan x, arcsin x, arccos x, arctan x. π 2 sin 1 x π 2, 0 cos 1 x π, π 2 < tan 1 x < π 2 1 (1) (
6 20 ( ) sin, cos, tan sin, cos, tan, arcsin, arccos, arctan. π 2 sin π 2, 0 cos π, π 2 < tan < π 2 () ( 2 2 lim 2 ( 2 ) ) 2 = 3 sin (2) lim 5 0 = 2 2 0 0 2 2 3 3 4 5 5 2 5 6 3 5 7 4 5 8 4 9 3 4 a 3 b
29
9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n
Chap9.dvi
.,. f(),, f(),,.,. () lim 2 +3 2 9 (2) lim 3 3 2 9 (4) lim ( ) 2 3 +3 (5) lim 2 9 (6) lim + (7) lim (8) lim (9) lim (0) lim 2 3 + 3 9 2 2 +3 () lim sin 2 sin 2 (2) lim +3 () lim 2 2 9 = 5 5 = 3 (2) lim
( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x +
(.. C. ( d 5 5 + C ( d d + C + C d ( d + C ( ( + d ( + + + d + + + + C (5 9 + d + d tan + C cos (sin (6 sin d d log sin + C sin + (7 + + d ( + + + + d log( + + + C ( (8 d 7 6 d + 6 + C ( (9 ( d 6 + 8 d
D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y
5 5. 2 D xy D (x, y z = f(x, y f D (2 (x, y, z f R 2 5.. z = x 2 y 2 {(x, y; x 2 +y 2 } x 2 +y 2 +z 2 = z 5.2. (x, y R 2 z = x 2 y + 3 (2,,, (, 3,, 3 (,, 5.3 (. (3 ( (a, b, c A : (x, y, z P : (x, y, x
高校生の就職への数学II
II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :
9 ( ) 9 5 I II III A B (0 ) 5 I II III A B (0 ), 6 8 I II A B (0 ), 6, 7 I II A B (00 ) OAB A B OA = OA OB = OB A B : P OP AB Q OA = a OB = b () OP a b () OP OQ () a = 5 b = OP AB OAB PAB a f(x) = (log
I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si
I 8 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No. : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin.
(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z
B 4 24 7 9 ( ) :,..,,.,. 4 4. f(z): D C: D a C, 2πi C f(z) dz = f(a). z a a C, ( ). (ii), a D, a U a,r D f. f(z) = A n (z a) n, z U a,r, n= A n := 2πi C f(ζ) dζ, n =,,..., (ζ a) n+, C a D. (iii) U a,r
sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
08 No. : No. : No.3 : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : No. : sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin
[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
![[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s](/thumbs/94/118579915.jpg "[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s")
[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
I 0 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd
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