I

0

( C) 80 35 0 30 60 90 0

0 0 03 _ fi 64 ;3!; (5 ' ) ' a>0b>0 a a =a + a a =a - (a ) =a (ab) =a b log 4 log ;4!; a>0a+ N>0 a =N HjjK =logån 3 f()=3+ f:x Y Y =f() X f

3 4 5 0 4 8 = =a a>0 a= =a (a>0a+) a = ={ } ;3!; 3 =3 =fi =(-5) =' 3

= -3 - - 0 3 = ;8!; ;4!; ;!; 4 8 () = 8 6 = = 4-3- - O 3 =f(-) =f() = ={;!;} a>0 a+ =a a a> 0<a< =a =a a :: a - :: a O - a O =a (a>0a+) a> < HjjK a <a 0<a< < HjjK a >a =a a>0a+ a> 0<a< (0) 4

= = - =- =f(-m) =f() m = - = = - = = - O 3 =-f() =f() =- = =- = =- - O - =3 =3 - =-3 + ={ } + 3 =-{ } + 3 { - } = + +3 = + +3 = - 3 =- = +3=4 = = +3= { 4 } 4 = + +3 = 5 4 3 - O { 4 }4 5

{ - } ={;3!;} - - a>0 a a =a + =X X X { - } =4 - + -3 = =3 =5 =5 - ={;5!;} =5 - { - } = + ={;!;} - 3 ={ } 3 ={ } +3 ==3 4 3 ={::} +3 3 ={::} O 3 = =3 6

(Bte) IEC IEC 04 Ki 04 Mi 04 Gi 04 Ti 0 = =log =f() =f() =a (a>0a+) =a HjjK =log a (a>0a+) =a =log a (a>0a+) =log a a 7

f f - =logå (a>0a+) =a (a>0a+) = =logå =a = `a> =a = a =logå O a `0<a< =a =logå a O a = = =log =log = = = =log O = = =log ={;!;} =log ;!; =log =log ;3!; =logå(a>0a+) a> 0< < HjjK logå <logå 0<a< 0< < HjjK logå >logå =log a a>0, a+ a> 0<a< (0) 8

=log =log (-) =log (-) =f(-m) =f() m =log (-) =log =log (-) O =log =log (-) =f(-) =f() =log (-) =log =log (-) =log (-) -- O =log =log =log (+) =log ;3!; (-) =log (-)+ =log ;3!; (-)+ 3 { 7} =log (+)+ =log (+)+ =log - 5 3 =log (+)+ =log = =log +=+=3 =7 =log 8+=3+=5 - O 7 { 3 5} 5 3 { 3 5}53 9

[ -;3!; ;3&;] =log ;3!; {+;3@;}+ log =X X X [ ;4!; 8] =(log ) -log -3 =log =log (-) =log ;5!; =log - [ ;8!; 4] =log - =log ;!; + f()= - +g()=log (-)+ = f()= - + g()=log (-)+ O O 0

00 f() f()=00 800 800 00 =800 ` 00 =8 = =3 a>0a+ a =a HjjK = 3 + =7 3 + =3 +=3 = a>0 (a ) =a a - = 3 a m 3 n a = n "ça m (mn ) - =;8!; 9 =3'3 {;9!;} - =7 4-3 = 4-3

4-3 +=0 4-3 +=0 ( ) -3 +=0 =X(X>0) X -3X+=0 (X-)(X-)=0 X= X= = = =0 = =0 = 3 =X X>0 9-8 3-9=0 3-5 3-3=0 Iº d m I I =Iº 4-0.d ;6 4;Iº m log (+)=3 a>0a+n>0 a =N HjK =log a N log (+)=3 += = - += =7 + += +>0 >- log (+)=3=7

a>0a+ [] logå=b HjjK =a (>0) [] logå =logå HjjK = ( >0 >0) >0 log =4 = =6 log 3=log 3= =4 log 3 (+)= log (3-4)=log 5 log (+3)=+log (log ) +log -=0 a>0a+m>0 N>0 log a a= log a MN=log a M+log a N +log =log +log =log log (+3)=log +3= =3 +3>0>0 =3 (log 3 ) +log 3 -=0 log 3 =X X +X-=0(X+)(X-)=0 X=- X= log 3 =- =3 - log 3 = =3 = =3 9 >0 = =3 9 =3 = =3 9 3

a>0a+m>0 log a M k =klog a M ( k ) log 3 (+5)=log 3 (-)+ (log ) -log 3-4=0 A B F B F=0 log A -0 0.05 <8 = 8 = =8 <8 3 <8<3 O 3 =a (a>0a+) [] a> a <a HjjK < [] 0<a< a <a HjjK > <'8 < ;#; <;#; {;!;} >; 6; {;!;} >{;!;} <4 4

4 <' { } + >{ } 5 3 3 4 - < -7 0. <0.00 3 3-3 +7 0 3-3 +7 0 (3 ) - 3 +7 0 3 =X(X>0) X -X+7 0 (X-3)(X-9) 0 3 X 9 3 3 3 4 - -æ0 9-5 3-3<0 50 % ;!8; n n log <3 =log log 8=3 log <3 0 8 log <30<<8 3 =log O 8 5

=logå (a>0, a+) >0 [] a> logå <logå HjjK 0< < [] 0<a< logå <logå HjjK > >0 log (+)<log 5 0<+<5 -<<4 log ;!; 3<log ;!; 5 3>5 >5 log (+)< log ;3!; (-)<- 4 log (-)<log 4 (3-) (log 3 ) + log 3-8<0 a>0a+b>0 c>0c+ logå b= logç b 4 logç a -4=-4log 3 =log 3-4 =log 4 3 log (-)<;!;log (3-)log (-)<log (3-) log (-) <log (3-) (-) <3- --<0(+)(-)<0 -<< ->03->0 <<3 << (log ) +log -8<0 log 3 =X X +X-8<0(X+4)(X-)<0-4<X< -4<log 3 < log 3 4<log 3 <log 3 3 3 4<<9 8 >0 4<<9 8 << 4<<9 8 6

log ;4!; (3+)<log ;!; (-) (log ) -log -<0 00 30 0 t30 A(t) A(t)=40+5log t ( t 0) 30 85 - =;4!; {;3!;} - ={;9!;} - log (-)=- log ;9!; (-)=log ;3!; + <8 {;!;} -6 >{;8!;} - log (-)> log ;3!; (-3)>log ;3!; (7-) abc a f() =b g() HjjK f()logça=g()logçb 3 = 3- =3 7

. =a (a>0a+) a. =logå (a>0a+) a 3. =a (a>0a+) =logå (a>0a+) 0 = + -3 =9{ } - 3 0 { - } = - 3 03 4 =log - =log {- } 04 =log (-)+log (+8) 8

05 5=0.5 3-3 - -=0 + log (+)=3 log (-)=logª(4-) 06 4 <'8 { } æ '4 log ;!; (-)> (log ) -4 log +3<0 07 =a b c =9{3 -;3!;}- abc ( a>0) 08 ab =logå=log A=logå b B=log a C=log b a O =logå =log 09 64 % 00 g50 g 50 g 0.05 % 9

00 8 9 6 77.8 7.7 W/m m W W/m =0 log3 0 70 70 W/m 30

0 0 [{ } «] {«} {r«} r >r=- r <r= f(+h)-f() f()= h 0 h f(a+h)-f(a) f '(a)= h 0 3 h 3 = +- =(+)( +3) n («)'=n«f()g() { f()g()}' =f '()g()+f()g '() 3

ee ln = 3 O = =a (a>0a+) [] a> [] 0<a< a = a =0 - a =0 a = - a =a a = 0 a> =a 0<a< =a a O a O = = =0 - { } = { } =0 { } = - 3

3 { } 3 4 4 - - 3 + 3-0<a< a =0 {;3@;} =0 3 +{;3@;} 3 + +0 = = 3= 3 - -0 -{;3@;} +3 +3 4-5 3 4 +5 logå >0 logå logå 0- - =logå (a>0a+) [] a> [] 0<a< logå= logå=- logå=- logå= 0+ 0+ logå =0 logå = a a> =logå 0<a< O a O a =logå 33

log =log = log = log =- log ;!; =log ;!; =- log ;!; =- log ;!; = 0+ 0+ log log ;3!; 4 log log ;9!; 0+ 0+ {log (+)-log } M>0N>0 logå M-logå N M =logå 3 N ( a>0a+) + {log (+)-log }= log 3 {log (+)-log }= log {+ } {log (+)-log }=log = {log (3+)-log 6} {log -log (9+)} e {+ } n n=3 n n {+ } n n ={+ }.7888845 e n {+;n!;} «.0000000.500000 3.3703704 0.593745 00.704838 000.76939 0000.78459 34

{+ } =e =t t 0 t 0 t (+t) =e e {+ } =e (+) 0 =e 3 {+ } (+3) ;[!; 0 {+ } = {+ } ;{;_ {+ } = [{+ } ;{; ] =e (+3) = (+3) ;3 [;_3 0 0 (+3) = [(+3) ;3 [; ] 0 =e e e {+ } (+) ;[!; 3 0 0 ab f()=(+a) ;[B; 0 f() 35

e e ln natural logarithm e log e (>0) e ln e = ln=log =0lne=log e= >0>0 ln =ln -ln ln «=nln lne ln'e ln ln e 'e 4 ln(+) 3 ln{+ } 0 ln (+) 0 3= 0 ln(+) = ln(+) ;[!; 0 =ln e= ln{+ } = ln[{+ } ] =ln e = 3 ln(+) ln{+ } 0 36

5 0 e - e -=t =ln (+t) 0 t 0 0 e - t = t 0 5= ln (+t) = t 0 ln (+t) ;t!; t 0 ln (+t) 4 t = = ln e e - 0 e - 0 3 5 3 + +4 4 +3 3 log ;!; {+ } {ln -ln( +)} (+) ;[@; e - 0 0 4 3 a>0a+ a logå(+) 0 43 a - 0 4 37

D +D =e D 0. 0.0 e. -e 3=.85884.- 0.00 0.000 =e 0 e - = e +h -e '= = h 0 h '=e h 0 '=e =e e h - h d e =e (e )'=e d h 0 e (e h -) h 0 a - =lna =a (a>0a+) a +h -a '= = h 0 h '=a h 0 '=a ln a a h - h h 0 d a =a ln a (a )'=a ln a d a (a h -) h 38

=e '=e =a '=a lna (a>0a+) = +3 =e = e f()g() { f()g()}' =f '()g()+f()g '() '=( )'+(3 )' =+3 ln3 '=()'e +(e )' = e +e =(+)e '=( )'e + (e )' =( ln )e + e = e (ln +) '=+3 ln 3 '=(+)e '= e (ln +) e + =e e =( ) =4 =e +5 =e ± =(+)e = 500 t 500 { 4 } t 5 4 ln0.8=-0.3 39

=ln ln(+h)-ln +h '= = ln h 0 4 h h 0 h h '= ln{+ } h 0 h h =t h 0 t 0 (+) ;[!; =e 0 h '= ln{+ }= ln(+t) h 0 5 h t 0 t '= 3 ln(+t) t 0 t '= ln(+t) t t 0 '= lne= d ln= (ln)'= d a>0a+b>0 c>0c+ logå b= logçb 4 logça =logå (a>0a+) log ln logå= 3= 5 log a lna ln '={ } ' 5 = 5 (ln)' lna lna '= 5 = 5 lna lna d log a = 5 (logå)'= 5 d lna lna =ln '= =logå (a>0a+) '= lna 40

= ln =+log '=()' ln+(ln)' '= ln+ =ln+ '=()'+(log )'=+ ln3 '=ln+ '=+ ln3 log =log +log ln3=ln3+ln =ln+log =log =(+) ln =ln3 =0 =+e =e =log º =+ln =ln 000 C t f(t) f(t)=000e kt (k=-._0-4 ) t=0 t C g 4

. {+ } {+ } =. e log (>0) 3. (e )'= (a )'= (a>0a+) 4. (ln)'= (logå)'= (a>0a+) 0 4 + log ( ++3) {log (-)-log ( -)} -3 5 ± +3 ± + 0 (-) {ln(+)-ln} 0 e 03 lne +ln'e lne+lne +lne +lne ++lne 04 0 e +a =b ab + 4

05 =e +3 = + ln 06 f()=ln+ln+ln3++ln0 f'() f'{;5!;} 07 e +e +a 4 (+0) f()= [ b (=0) ab 08 0 a +b - 3 =ln4 ab (ab) 09 a =ln(+) =a=3a AB O A a 0+ OB A O a =a =ln (+) B 3a =3a 43

e A r A(+r) r 6 r A{+ } r 4 3 r A{+ } 3 r 4 r A{+ } r A 3 n n n 44

0 = = = - =6 {;!;} - 8 3- =a m n -n=a -m (a>0a+) 0 8 4 {;!0(;} 5 {;!0(;} 3 '3 ' 0<a< m<n HjK a m >a n a> m<n HjK a m <a n 03 =log (+a)+b ab ( =) =log (+a)+b =log a (+m)+n =-m O 04 8 =(log ){log }+5 log =X X 05 f()={;3!;} g() (gágáf)()<0 f()g() (g Á f)()(f Á g)() 45

06 e - (3-) 0 4 3 + - 0 0 (+) ;[!; =e e - = 07-4 - log - -4 f()-f(a) f'(a)= a -a f'(a)= h 0 f(a+h)-f(a) h 08 f()=e (ln+a) f()-e 3=b ab - f()g() { f()g()}' =f'()g()+f()g'() 09 a + ( ) f()= = ab ln+b (>) f() =a =a 0 50 f() f()=50 ;3{; 3 f'(3) = h 0 f(3+h)-f(3) h 46

= +3 = -3 ^ ^(+3) = =h() -3 = +3 = +3 = 3 47

=;6!; -;3@; P(0) Q{t ;6!;t -;3@;t} H(t 0) PQ =:: -:: 6 3 Q h Q P tanh O t> QH ;6!;t -;3@;t ;6!;t(t-)(t+) tan h= = t- = t- =;6!;t(t+) PH tan h= ;6!;t(t+)=;3$; t + t + P h H(t, 0) tan h ;3$; =;6!; -;3@; P(0) =e P(0)Q(te ) PQ = h Q P tan h e =e Q t>0 = P h O t =ln P(0)Q(t ln t) PQ h Q P tan h ln t O P h =ln Q t t> 48

66 { ;5@;} 4 4 8% 04 n _{+} n 388 04 4 4_(+0.08) 388 3 0 0 03 0 0 49