Chap4 part2

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1

: 111 anxn+a1x+a0yx(a,b)exlog(x): 2

a1xx2 4-5 4-5 y=ax, a1 y=exa=e2.718282 y=( )x : R (0,)

: 33 4-5

3-1 :: 44 4-5 y=logax, a1 y=logex=ln(x)a=e2.718282 : (0,) R

, a1y=log(x) x=aya : 55: 4-5 : log2(32)=5 32=25log3( )=-2 = 3-2

: 10 log10x=logx : log 0.001=-3 0.001= = = 10-3110001103

: 66: ...

log4(4)(3). (1)

(2) log2(32)+log6(36)-log5(625).

(6) :

(3) ln(125)-ln(25). (2)

4-5 : 77 4-6

: .

(1): am=an ( a1 a>0) m=n. ( )

(2): xm=ym ( m0 m ) x=y.( )

: x 4-6

(1)(2)

: 8 4-7

y=f(x) :(1) f(a)=f(b) a=b (2) ab f(a)f(b)

: f(x) : f(x) 4-7 (1) (2)

: 9 y=f(x) Y X. 4-7 X Yf

X YfX Yf

: 10X Yf

X Yf

X Yf 4-7 : 11 y=f(x) y=f(x) x=f -1(y) :(1) f -1(x) f(x)(2) f -1(x) f(x)

(3)

: x[3/2 , ) : ( ) ( ): x : x y y x ()

4-7 : 1212 4-8

: 3000 100 80 500 . . :x ( ) y ( x ) (x,y) : : 100 3000 4-8

: 13 : 80 3500

: (1) =m

(2): x=100 y y(100)=-25(100)+5500=3000 book per day y(80)=-25(80)+5500=3500 book per day

4-8 : 14: p t (1) p(t)=30000+2000 t1) 2) 3) 50,000 1) ( ) t=0 p(0)

2) t=1 p(1)

( t=0 t=1) p(1)-p(0)=20003) ( ) p(t) p(t)=50000 (1)p(t)=50000=30000+2000 t 2000 t=20000 t=10 years : 50000 10

4-8 : 1515

4-8 : 1616

4-8 : 1717

4-8 : 18: D P 25 1200 85 1000 :

(1) D(P) (P1,D1) (P2,D2) (1200, 25) (1000,85)

( )

4-8 : 19(2) 1100

P 1100 P=1100 D(1100)=-0.3(1100)+385=55

4-8 : 2020 S(P)=A+ B P S P ()A (S(0)=A)B

4-8 : 2121

4-8 : 2222

4-8 : 2323 ( ) : P ( ): S(P)=30+7 P D(P)=128-3 P P S(P) D(P)

P S(P)=D(P) 30+7P=128-3P P=9.8 Riyal . ( ) S(P=9.8)=S(9.8)=30+7(9.8)=98.6 4-8 : 24 4-8 COST CONS COST(q)=A + B qq: A: B: ( ) CONS(I)=A + B I I:

: 100000 25 40000 COST(q)=40000+25q 30000 . q=30000 COST(30000)=40000+25(30000)=790000 Riyal 790000/30000=79/3 Riyal: 25

: D(x)=550 (0.9)x x D 20

x thousands D(20)=550(0.9)20=66.8672

66867 1000 ): 2626

123: 27

: : 0124097

0124097 ( 10 ) 1: 28 :

:

:

: : :

: : :

2 A 0124097 111MATHAE 121210 A A : 293

(1) (2) (3) (4) (5) (1) 5 20