? 1c±s  5 ±s?? ? ???1 1cm ￥M oV ?1Ba¨1 0.01cm ￥^ k¨ p± s￥ZE ? ?o o31¨^  X$ ^￥ á1 8.9g/ b 3 cm 3 o8 3 3 4 rV π=  ?o o^ ?31^￥é 1 12.14 2 ≈?≈?= rrVm ρπρ gb ? ¨?l￡ üf ? yx= 2 3  ?￥???l×?"  x = 0?B ?-?? ^ V±￥b ￡ ? H0x = 3 2 xy ?=? ^ x? ￥?¨í kl ? [ yx= 2 3  ? V ±b? H 0x = 0x ≠ 322333 3 33 33 2233 3 () ( )( 2 (), 3 () yxx x xxxxxx xxx 3 ) x xox x xx xxx x ?= +? ? = +?+ +?? +? + =?= +? + +? + ? ?[ yx= 2 3  ^ V±￥b 0x ≠ 57 5 ? ?￥il??é 1 ! i p/ ò T￥′ ′fx() 0 ò lim ()( ? ? ? x fx x fx) x → ? ? 0 00  ó lim () ( ) xx fx fx xx → ? ?0 0 0  ? lim ()() h fx h fx h h → + ?? 0 00 b 3 (1) )(' )( )())(( lim )()( lim 0 00 0 00 0 xf x xfxxf x xfxxf xx ?= ?? ???+ ?= ? ??? →?→? b ó )(' )())(( lim )()( lim 0 0 000 0 0 0 00 xf xx xfxxxf xx xfxf xxxx = ? ??+ = ? ? →?→ b ? h hxfhxf h )()( lim 00 0 ??+ →  )('2 )()( lim )()( lim 0 00 0 00 0 xf h xfhxf h xfhxf hh = ?? ? ?+ = →→ b 2 ò ¨?l p ?tL yx x= + ?23 2 1￥?f ? ó p? ?tL V? (,)? ?12)￥ MLZ? ? p? ?tL V? (,)?21)￥ELZ? ? ù? ?tL  ^?μ (, V??￥ MLD ?tL??D? ?￥ ?L ü?$ )ab 3 (1)y1 xx x xxxxxx x y ?++= ? ?+???++?+ = ? ? 234 )132(1)(3)(2 22  ?[ 34lim)(' 0 += ? ? = →? x x y xf x b (2)?? 1)1(' ?=?f  MLZ?1 1[ ( 1)] ( 2) 3yx x=?? ?? +? =??b (3)?? 5)2(' ?=?f ELZ?1 17 [(2)]1 55 x yx + =? ? ? + = ? b (4) ?tL??D??￥ ?L ü?? yà '| q1í kv ? (1) V 58 ??i x P¤  ?[?"￥? ?ib ∞=)(' xf (,)ab 3 ! 1 ￥ V?f ? O)(xf ),( +∞?∞ 0=x ￥ ? #× ? ? )(8)sin1(3)sin1( xxxfxf α+=??+  ? )(xα ^? H1 ú¨￥í klb p wL0→x x )(xfy =  )￥ MLZ?b ))1(,1( f 3 : )sin1(3)sin1()( xfxfxF ??+=  V ¤ 0)1(2)(lim 0 =?= → fxF x ' b ? 0)1( =f 00 () 8 () lim lim 8 xx Fx x x x x α →→ + ==D 00 0 ( ) (1 sin ) (1) sin (1 sin ) (1) sin lim lim 3lim 4 '(1) sin sin xx x Fx fxfx fxfx f x x →→ → +? ????? =?? ? ??? ??? ? = ? ?  ¤? b? ^ wL  )￥ MLZ?1 b 2)1(' =f )(xfy = ))1(,1( f )1(2 ?= xy 4 ￡ ü V??￥B????￥ ?B ?;L ü??Q a Q ;A?üV ?￥ 6B???b  nm 4.2.5 ￡ !??Z?1 01 2 2 2 2 >>=+ ba b y a x  ??US1 22 ),0,( bacc ?=± bL ! 1??  ?iB? ? H2 ?A ?? ?b C ! ),( 00 yx 0 0 =y 0 0 ≠y  5 VN?￥ M L | q1 0 2 0 2 tan ya xb ?=θ  D??),( 00 yx )0,( c? ?L￥| q1 cx y + = 0 0 1 tanθ  N ?LD MLC?￥? M1 θθ θθ tantan1 tantan 1 1 + ? =k b ?¨ ? 222 bac ?= 1 2 2 0 2 2 0 =+ b y a x } ?9 ?¤? 59 2 00 22222222 000 0 2 22 2 2 2 00 00 0 00 0 0 2 00 () 1 ybx xcay aybxcxb abcxb b k ybx a b xy acy cxy acy cy xcay + ++++ == = ?+ + ?? + =b ),( 00 yx D 6B?? ?L￥| q1)0,(c cx y ? = 0 0 2 tanθ N ?LD ML C?￥? M1 2 00 2222222 00 0 0 0 02 2 22 2 2 2 0020 2 00 tan tan 1tantan ( ) 1 bx y ay x c cxb ay bx cxb ab b k ybx abxyacycxyacycy xcay θθ θθ ?? ??? ?? == == +? ?? ? 0 =b ?? ?C?￥? MM? ?[ ?C?M? 5¤￡b 5 ￡ ü ? wL  ?B?)￥ MLD USà?￥°? ? ??￥ ??1 b xy a= 2 2 2 a ￡ L ! 1 ? wL  ?iB? 5  V?B?￥ ML| q1 ),( 00 yx 2 00 ayx = 0 0 2 0 2 0 ' x y x a y x ?=?=  MLZ?1 )( 0 0 0 0 xx x y yy ??=?  ^¤ MLD USà￥??1 ? b MLD USà? ￥°? ???￥ ?1 )2,0( 0 y )0,2( 0 x 2 0000 22)2)(2( 2 1 ayxxyS === b 6 pf ?? V??)￥P? ??·? ?b ò y = |sin |x  ó yx=?1cos ? y x = ? e ||  ? yx= +|ln( )|1 . 3  1 ?y = () |sin |fx x= 0=x H 60 1 sin lim |0sin||sin| lim)0( 00 ' = ? ? = ? ?? = +→?+→? + x x x x f xx  ' 00 | sin | | sin 0 | sin (0) lim lim 1 xx xx f x x ? ?→? ?→? ? ? ? ? ?  ?[ ^? V??b???f ? y ^? ù10=x π￥f ? ?μ? V? ?1 )( Zkkx ∈= π  O 1)( ?=′ ? πkf   1)( =′ + πkf b  2 y = () 1 cosfx x=? 2 2sin 2 sin 22 x x ==? 1 V?? V? ? 1 )(2 Zkkx ∈= π  Oü9 ?¤? 2 (2 ) 2 fkπ ? ′ =?  2 (2 ) 2 fkπ + ′ = b  3 ? V??oμ || () e x yfx ? == 0=x  O 1 1 lim)0( 0 ' ?= ? ? = ?? +→? + x e f x x  1 1 lim)0( 0 ' = ? ? = ? ?→? ? x e f x x b  4 ()yfx== )1ln( +x ? V??oμ 0=x  O ' 00 |ln( 1)| ln1 ln( 1) (0) lim lim 1 xx xx f x x + ?→+ ?→+ ?+ ? ?+ = = ? ?  ' |ln( 1)| ln1 ln( 1) (0) lim lim 1 xx f x x ? ?→? ?→? ?+ ? ? ?+ =? ? ? b 7) ?/ f ? x = 0)￥ V?? ò ? ? ? = ≠> = + ;0,0 ,0)0(,sin|| 1 1 x xax y x a ó y xx ax b x = > +≤ ? ? ? 2 0 0 ,, ,; ? y xx ax x x = > ≤ ? ? ? e, , ,; 0 0 2 ? y x x a x = ≠ = ? ? ? ? ? e, ,. 2 0 00 , 3  1 1 00 0 1 ||sin 1 lim lim lim | | sgn( )sin 0 a a xx x x y x xx xx x + ?→ ?→ ?→ ? ? ?? ==?? ?? ?? ?? = ?[f ?  V?b 0=x  2 ?Tf ? V? 5A?0=x 0=x ?? ? V¤ b? H bff ==+ )0()0( 0=b 0=b 0 0 lim)0( 2 0 ' = ? ?? = +→? + x x f x  a x xa f x = ? ?? = ?→? ? 0 lim)0( 0 '  61 #? Hf ? V?  e f ?/f ?0==ba 0=x 0=x ? V?b  3?? 1 0 lim)0( 0 ' = ? ?? = ? +→? + x xe f x x  )0(0 0 lim)0( ' 2 0 ' + ?→? ? ≠= ? ?? = f x xa f x  #f ? ? V?b 0=x  4? Hf ?0a≥ 0=x ? ?? ?[? V? ? H 0a< 2 00 0 lim lim 0 a x xx ye xx ? ?→ ?→ ?? = ?? = ?[? 0<a Hf ? 0=x V?b 8 ! fx() x = 0) V? I 1 f ?/ |( )|fx x = 0)9 V?$ 3 ? H?^ ! 50)0( ≠f 0)0( >f x = 0￥l #×?μ  #  ?[ |(  0)( >xf )(|)(| xfxf = )|fx x = 0)9 V?b ? H?? 0)0( =f |()||(0)| () (0) sgn 00 fx f fx f x xx ?? = ??  sY x = 0)9 ?Pa·K¤? |( )|fx x = 0)￥P? ?1  ·? ?1 |'  ? [ |( |'(0)f? | (0)|f )|fx x = 0)9 V?￥ sA1H q ^ b '(0) 0f = 9 !  [,  ??fx() ]ab fa fb() ()= = 0 O 0)()( >′?′ ?+ bfaf ￡ ü  (, à iB? ,?b fx() )ab ￡ ?5 !? )(af + ′ ? ]|?^ ! ??1? ?b?? )(bf ? ′ ' () () () () lim lim 0 xa xa fx fa fx fa x axa + →+ →+ ? ==> ? ?  V?i 11 ()x axb< <  b ] ??? 0)( 1 >xf ' () () () () lim lim 0 xb xb fx fb fx fb x bxb ? →? →? ? = = ?? > V?i 21 2 ()x xxb<< b? ??f ?￥ ,?i? ? f ?  -Wμ ,?b 0)( 2 <xf fx() 21 , xx 10 ! μK uW = V? fx() (,)ab 62 ò ?  * 1 ???9μlim ( ) xa fx →+ =∞ lim ( ) xa fx →+ ′ =∞$ ó ? lim ( ) xa fx →+ ′ =∞ * 1 ???9μ lim ( ) xa fx →+ =∞$ 3 1?B?bQ è xx xf 1 cos 1 )( +=  0=a   0 lim ( ) x fx →+ =+∞ ) 1 sin1( 1 )(' 2 xx xf +?=  ∞= +→ )('lim 0 xf x ?? ?b  2?B?bQ è xxf =)(  0=a  00 1 lim ( ) lim 2 xx fx x →+ →+ ′ = =+∞7 0 lim ( ) 0 x fx →+ =≠∞b 11 ! f ? ?@ b￡ ü )(xf 0)0( =f )(xf 0=x ) V?￥ sA1Hq ^i ) ??￥f ?  P¤0=x )(xg )()( xxgxf =  ON H? ? b )0()0( gf =′ ￡  s?b ? V?)()( xxgxf = 00 () (0) lim lim ( ) (0) xx fx f gx g x →→ ? ==#  )(xf 0=x ) V? O? ? )0()0( gf =′ b A1?b 7 ? ? ? ? ? = ≠ = 0),0(' 0, )( )( xf x x xf xg 5 )()( xxgxf =  O 00 () (0) lim ( ) lim '(0) (0) xx fx f gx f g x →→ ? ===' )(xg 0=x ) ??b 63