??cf ? x1 ü à T 1./ f ?x = 0￥{ |e v?[￥ ü àZ 7 T (1) e2x (2) cosx2 (3) ln(1?x) (4) 1(1+x)2 (5) x3+2x+1x?1 (6) sin3 x (7) x2x2+x?1 (8) ln 1+x1?2x 2/ f ?x = 0￥ ü à Tà ?·￥¨ ? (1) esinx;(x3) (2) lncosx;(x6) (3) xsinx;(x4) (4) x2p1?x+x2;(x4) 3 p/ f ?x = 1￥ ü àZ 7 T (1) lnx (2) ax 1 (3) P(x) = x3 ?2x2 +3x+5 4 ??è ?a;b Px ! 0 H (1) f(x) = (a+bcosx)sinx?x1x￥5¨í kl (2) f(x) = ex ? 1+ax1+bx1x￥3¨í kl 5 ?¨ ü à T pK (1) limx!1?1x ? 1sinx￠ (2) limx!1 ? ex3?1?x3 sin6 2x ·  (3) limn!1?n+ 12￠ln?1+ 1n￠ (4) limx!1 1?cos(sinx)2ln(1+x2) (5) limx!1( 3px3 +3x?px2 ?2x) 6 !f(x)e?￥ #×=Q V? O limx!1 sin3x x3 + f(x) x2 ? = 0 (1) f(0);f0(0);f00(0) (2) limx!0 ? 1 x2 + f(x) x2 ·  7 !f(x) Là  ?iQ V? 7F(x) = f(x2) p￡ F(2n+1)(0) = 0; F (2n)(0) (2n)! = f(n)(0) n! : 8 !P(x)1BnQ[ T (1) P(a);P0(a);￠￠￠ ;P(n)(a)￥1? ?￡ üP(x)(a;+1) í? (2) P(a);P0(a);￠￠￠ ;P(n)(a)?μ|MW￡ üP(x)(?1;a) í? 2 9 p￡ (1) e = 1+1+ 12! +￠￠￠ 1n! + e (n+1)!(0 < < 1) (2) e ^í ? ? 10 !f(x)[a;b] μ=¨? ? Of0(a) = f0(b) = 05ic 2 (a;b) P jf0(c)j> 4(b?a)2jf(b)?f(a)j: 11 !f(x)a??í=Q V? Of00(a) 6= 0?±s?′? ? f(a+h)?f(a) = f0(a+ h)h;0 < < 1 p￡lim h!0 = 12 12￡ ü ?f ?f(x) uW[a;b] ?μf00(x) ? 05[a;b] = ?i ?x1;x2?μ f(x1)+f(x2) 2 ? f( x1 +x2 2 ): x2±s+?Dt ??￥?¨ 1 p/ ò wL ???￥m? ? (1) y2 = 4(x+1); y2 = 4(1?x); (2) y = jlnxj; y = 0 (0:1 6 x 6 10); (3) y = xy = x+sin2 x (0 6 x 6 …); (4) y2 = 2x;x = 5; (5) y = x2;y = x+5; (6) x23 +y23 = a23. 3 2 p/ ¨USV U￥ wL ??m?￥ ? (1) ? gLr2 = a2 cos2’; (2) ?= o>Lr2 = asin3’; (3)Lr = acos +b. 3 p/ ¨? ?Z?V U￥ wL ??m?￥ ? (1) x = 2t?t2;y = 2t2 ?t3; (2)?Lx = a(t?sint);y = a(1?cost)(0 6 x 6 2…)#xà (3)?￥v 7Lx = a(cost + tsint);y = a(sint?tcost);(0 6 x 6 2…)# ?°Lx = a(y 6 0) ?a > 0 4°Ly = xü??x2 + 3y2 = 6y￥ ?s? ?sA(l￥B v)?B(￥B v) pAB-′ 5 pr = 3cos ?r = 1+cos ??￥ ?s￥ ? 6 p/ è8￥8 ??x2a2 + y2b2 = 1 ?xà (2) y = sinx;y = 0(0 6 x 6 …) (i) ?xà(ii) ?yà (3)è }Lx = a(t?sint);y = a(1?cost)(0 6 x 6 2…);y = 0 (i) ?xà(ii) ?yà(iii) ?°Ly = 2a ; (4) ? wLy2b2 ? x2a2 = 1D°Ly = §h ??￥m? ?xàè 7 p?/ ò w ? ???￥+?8￥8 4 (1) p?8￥8  /?￥1????￥àésY? ?AB?ab7ú1h (2)?? ?  /?sY ^??1aab￥?7 W￥  ?1h 8X? o??1R k pú1h￥ o38(h ? R) 9. p/  wL￥?é (1) y = x2; 0 6 x 6 1; (2) y = ex; 1 6 x 6 2; (3) px+py = 1; (4)??Lx = a(1+cos ); 0 6 6 2…;a > 0; (5)?￥v 7Lx = a(cost+tsint);y = a(sint?tcost);a > 0;0 6 t 6 2…; (6) r = asin3 3 (a > 0); (7)?#Lr = a(1+cos ); 0 6 6 2…;a > 0. 10 p/ ò wL·??￥ w q? w q?? (1) xy = 4?(22) (2) y = lnx?(10) 11 p/  wL￥ w qD w q?? (1) ?tLy2 = 2px; (2) ? wLy2b2 ? x2a2 = 1; (3)??Lx23 +y23 = a23. 5 12 p/ ? ?Z?ó￥ wL￥ w q? w q?? (1)è }Lx = a(t?sint);y = a(1?cost)a > 0; (2)??x = acost;y = bsint(a;b > 0); (3)?￥v 7Lx = a(cost+tsint);y = a(sint?tcost): 13 p/ [USV U￥ wL￥ w q?? (1)?#Lr = a(1+cos )(a > 0) ; (2) ? gLr = 2a2 cos2 (a > 0) ; (3) ? ?Lr = ae? (? > 0) . 14 ! wL ^¨USZ?r = r( )ó O=¨ V?￡ ü ?? ) w q1 K = jr 2 +2r02 ?rr00j (r2 +r02)32 : 15￡ ü ?tLy = ax2 +bx+c??)￥ w q??1Kl 16 p wLy = 2(x?1)2￥Kl w q?? 17 p wLy = ex  w qKv￥? 18 p/  ü ? wL ?àè ?¤è w ?￥ ? (1) y = sinx; 0 6 x 6 … ?xà (2) x = a(t?sint);y = a(1?cost)a > 0; 0 6 x 6 2… ?°Ly = 2a; (3) x2a2 + y2b2 = 1(a > b) ?xà (4) x = acos3 t;y = asin3 t ?xà (5) r2 = 2a2 cos2 ?à 6 19 p/  wL ￥é? (1)??1r?é112…fi(fi 6 …)￥ ( ?? (2) ? ?Lr = aek (a > 0;k > 0) ??(0;a)??( ;r)￥ ( ?   (3)[A(00)B(01)C(21)D(20)1??￥ ??? wL  ?B?￥ á?????e?  ?￥2 (4) x = a(t?sint);y = a(1?cost);0 6 t 6 2…;a > 0 á1è ? 20X?B ?tL y = x2(?1 6 x 6 1) wL  ?B?)￥ á D???yà￥  ???1x = 1) á15 pN wL ￥é  21àé10m ás?1‰(x) = (6 + 0:3x)kg/m ?x1 à￥B ? ?￥  ? pà￥é  22 p? o0 6 z 6pR2 ?x2 ?y2￥é? 23b p8px2 +y2 6 z 6 h￥é?? ?zà￥?8  24 p ?t8x2 +y2 6 z 6 h￥é?? ?zà￥?8  x3±sZ?? 1 p/ ±sZ?￥Y3 (1) xy0 ?ylny = 0; (2)y0 = q 1?y2 1?x2; (3) 3x2 +5x?5y0 = 0; (4) xydx+(x2 +1)dy = 0; 7 (5) y ?xy0 = a(y2 +y0); (6) (y +3)dx+cotxdy = 0; (7) dydx = 10x+y; (8) xsecydx+(x+1)dy = 0; (9) (ex+y ?ex)dx+(ex+y +ey)dy = 0; (10) ylnxdx+xlnydy = 0. 2 pXó±sZ? ?@ SHq￥+3 (1) dydx sinx = ylny;yjx=…2 = e; (2) y0 = e2x?y;yjx=0 = 0; (3) x1+ydy ? y1+xdy = 0;yjx=0 = 1. 3é 11g￥é? s ?T¨T°L?? ?? HW??1?é ??￥ ??Q1t = 10s H ???50cms ?14￡10?5N ùV? 7 SüV Bsòa￥ ? ^ ? 4 ?￥ ?Mμ ?/￥? p ?￥ ?M ?D ? ?Ci￥ R?? 1?ü? ? ?üV1600 Mao?e S Rb￥B? k p ? ￥ RD HWt￥f ?1" 8