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1.1 1.2 1.3 10 1.4 13 1.5 18 25 25 2.2 Nh 29 32 38 49 50 - Mathematics Thang Long University Libraty 1) 2) d g Thang Long University Libraty t n n 1.1 tranh Thang Long University Libraty y d x2 x x x kim S sun sun S s A p s P t sp Ap SP AP p T P TP sp SP y Thang Long University Libraty 1.2 Q P h Aristotle A' A B D' B' O C D C' Thang Long University Libraty n c th - 36 Q M cos r - y y D r= c r x O t x 37 Thang Long University Libraty cho n i - x x2 y n c 2.4 P1 2, P3, Pn 2, n+1 Q3, Qn, pn n n n [p1, q1], [p2, q2], , [pn, qn], , 38 qn pn (qn pn ) q2 p2 39 Thang Long University Libraty y= 2,4,8, ,2n k, tk+1 (b a ) f (tk ) 2n b a f tk 2n Sn' '' Sn ' Sn '' ' Sn Sn '' Sn (b a ) ( f (b) 2n f (a )) ' Sn , Sn'' y= xm cho Sn' Sn'' S bm a m m 40 y S2 S1 a O x b I m p/q -1) ( ) (C) D qua M M cong (C) D D M M O OM ng conic, 41 Thang Long University Libraty y xm D Y ax b M y xm ( x, y) P x h m OX RS h x m ax b D M C RS ( x h) m ( a ( x h) b) mhxm h Q ( x, h) ah h(mxm a hQ ( x, h)) Q(x,h cho |Q(x, h)| A, v i |h| 42 (*) x A Y D M R S O x+h x + hn mxm x P X a h < h h (*) / A, RS h h h D M a D0 mxm m x= 3, Do Y xm mxm ( X x) M 43 Thang Long University Libraty Y y = x3 O X 2n n n ( x,1 / x) 1/ n x n 44 OX hn x hn n (hn ) n0 a n0 a (hn a ) lim hn n a lim(ck bk ) 0, k bk (ck ) y xm mxm a (( x hn ) m hn xm ) M (5) M i hn x hn y hn f ( x) ( f ( x hn ) hn f ( x)) (6) hn x3 y2 , y sin x, y tan x, 45 Thang Long University Libraty ), hn n s x y f ( x) y dy / dx y x y f '( x) f ( x) f ( x) a b, b f (t )dt a I OX 46 x I x F ( x) f (t )dt a x y x f ( x) F ( x) F ( x) f ( x) ) h x h h f ( x) f (t )dt h f ( x h) x ta ( F ( x h) F ( x)) h f ( x h) f ( x) f ( x h) f ( x), h f ( x) h F ( x) f ( x) F ( x) C f ( x)dx f ( x) 47 Thang Long University Libraty Y f(x + h) f(x) h x x+h X i (theo 48 - Hilbert - 49 Thang Long University Libraty O 1) i ong 2014 2) 3) Mathematics the music of reason Springer, 1992 A Irvine Philosophy of Mathematics North Holland Publishing House, 2009 50