0000002140 00000 n 0000045091 00000 n 0000040330 00000 n

0000001694 00000 n 0000019290 00000 n

%���� ß×Oœ5ƒñéİ]­Š’‘o½zøL»+hjÔúµÀÇÇæ˜]®.ê�6ŵt­Ywœ`SÁ.ó"³É‡ø¶ ı‹Ï‹¿¿^ÆĞ5ì‰b1�‚%ÉæœEÉo�–}\‡­*xöùMrşÙLî®¶`Î1›núÖùzlYW|Ñ�”ÌæAnQ(S\.§/æ)¾3Ѻ•�_½œ@bDFíC1(ş~¥­)¡Ÿ§Ï. 0000107995 00000 n Notations. 0000107139 00000 n 5 0 obj 3. 54 0 obj <> endobj xref 54 68 0000000016 00000 n %PDF-1.4 0000024554 00000 n Let us now consider several classical Taylor series expansions. 0000013413 00000 n

0000029110 00000 n 0000106467 00000 n 0000028669 00000 n + 3!

Let us start with the formula 1 1¡x = X1 n=0 0000036157 00000 n . 0000044619 00000 n Use the last step to write out the first 8 (or more) terms of the series for eiθ. converges for all real x. *�R�q�ep���`�I����\0��7 �X?�5�%�d�8Ƒ�$:�^������G�n4�l��e�|���(�86���p���A"/n?��}��k���vq��D?��B���ZgK�c�ns��Z[��-�����l�ʵ����%E!U�ʫD����ф�C+5R���6i�?�,.��{vDy�m,�mu!�O���Jn?��D�`� *�2%�:�P�N< C�C��≸�zc+�ť��t�0{S�u��H}�w���$�R�7�5��*XCHl� ���#8Z����bD��׏랄j���n^}���Ib���H[Z�Xi����Ck��aը5�u���?F���߶u;����فS�=�z���*�|�;��w��|Qd�Ԡ�-�t���0eML����K�&�5�X���\�r��l��[c]`��M����IT����J��tQ��M)֙[c]���F�Ġ���"���Ƈɚ���2�p�B�v"M ��DH]� $bkL�NT�2�㝳9�������[�YA��uw��d�p��s29��,�8sD-�I��sAZj::v��j�D��������qe[d�Ҥ�{z��`1�RfRk�Fp�Xv�J��~VqJ�+�^kK?�*�nk�X�5�2��0�Yk����8��g�q����.�. The trick is to write f(x0+ x;y0+ y) = F(1) with F(t) = f(x0+t x;y0+t y) and think of x0, y0, x and y as constants so that F is a function of the single variable t. 0000023236 00000 n We now generalize to functions of more than one vari-able. -����&�X]^Wo�^�Z__�\�_������gW�g�}�r�|�����_��]�j�!���� g�Rc﷫o7��/M�ֺg��ؘ ���j3�����0m�lF"tG:U���F�a3+1Q,ls+6�|3�{i�`\r�3��Ƙ��&��;2��I��b �)ͨ?�Y㝫.0El3�z�Z�ӯ)�@�ے��-'� ���[����V�?�T��Tޣa����՛w����^�/,�����k����T�^��z��O�֖� 0000003002 00000 n :��d�O��y[,ŗ}Dg�1z����$H�vw����4K�+�6zM?��xY�"̴ ���8��(�cB`ߑp�����^A�����=� 1�L����U�`v~�%�u�}�y��++9p�1�&i!d,b�q�R��-j���"����3�$B�c�R$�K�Õ z뱳�DL����bTy��d�Q@�ޣ��86����J�i�C7�8k���{@�rҐ�!9��H�@�*��,�%E^�=�u"���t�a�M���9B�~�'u�3��E]5S�����0�5�6C�)��a������"7�]����OU��ä����0fV�uY*ՙY�*�il���ӺR����f%٨!y�=`�fF����\�`��T�]G�'��;��z��o%`��V�/�8r����Uގ�-_�Q��$�����m�`O��I���oe��� �D�[�9@�0�_�i��ٛ^1*3�|hv�v��L� ���;�P��w�k�Y+����E~����O��1�.����l ``}�/���,&��W5�N�lP��l���(��d�Pm�ƪ`��3�++����#�����S�s3��V���p���D� #_xG���)K+f��@��� �y�5�p��%{)�����% C�8�,n9zs�۷`�#d�]�9������@�_ Ecrivez la s erie de Taylor en 0 de la fonction x 7!cosˇx: Fonctions de base et s erie de Taylor Nous avons "cinq" fonctions de base.

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Taylor Series Expansions In the previous section, we learned that any power series represents a function and that it is very easy to di¤erentiate or integrate a power series function. 0000041014 00000 n x��=ٮǕ���̼���v���l ����7�C��JVlKW�d+���9�t���j�)+�ͮ��K�S�~�&�a�_�{������G/������Wn��$�V�믯�@��\O�m,����ۻ;1qg�߾�1If����O�0˷�w{>%������I8���?���Sv�My��>Z?y嶟«^p�w���Ĕ�:?�F�Y=��m_��MJ��_������Bha����R��|��z�������\?�Jr�m��?��(���>�uJ�����WdԳ�TDW����"\�����?퀔�O^k���s?��^��O �w ��R���!bX 0000108787 00000 n 0000019179 00000 n Calculus III: Taylor Series 647 tool here, but commutative diagrams in the homotopy category are relatively useless. 0000037928 00000 n O���q��>[�SR^��>�s�Q��X/��i��N-�8"��N�mPX���ZeM�:g� � iT�l �/NBD0v�-�p�r"r}�w�˷����,ݮj�c�n*���2x��4x�J��œ:3���f���:�}��m}�qT�t����:�ZtS�=��g- ���j��c�[�h�Fg`��8Fų�=�_7�N��Z�,U� ��C���)-}��Ň�b��z�ULT�R ��J��ۭ�:�L�U�Z_F�ϊ�,�ڙ�>�C�ݼ��׽0�=ڛ�9�زh0t�P�ZNMBQM��GK�l�ɱ��hJ:� ��@�DuC/�42)l]�tGH����@`�児z�Lr�|$Ќ3O!I��Y���@�\���tu���պ�����?t�&*�k�������E�� ���bNԥ2�B��^/�nj�Q'��V�� �����a"�p��������[��Ѡtp�q�J��̺[\�|%���Nf+�ۊ���e�q4�e��}��K[���T View Table of Taylor Series.pdf from MATH 2201 at University of Massachusetts, Amherst. %�쏢 Taylor series for tanx explicitly exhibits the factor of (−1)n, which is common to the Taylor expansions of all the other trigonometric functions. 0000019360 00000 n 0000004001 00000 n %PDF-1.4 %���� !u�R�Y���Ձ�&�%��# �`�~OF��n^Z��OpϜ�|y���d/p]7)X5O�< �Hmp��Z���:/��(���a�H;�+ �X���J��} oH;��c'����5�����H ؊28�09����?э��h�3\q_�C �$�#t"X��=}����M��_%:�%�k d)$H!Jx����r��J���v�~�5>��"�8��k`\g5������7����m�ܒ����+fE�j�4�^*��7{Tk�G"�0@2�PoA�$�6. + x8 8!

+ ::: e(17x) = P 1 n=0 (17 x)n! 0000031764 00000 n

<> 0000045605 00000 n + x4 4! 0000009070 00000 n just think of x as r = X1 n=0 xn x 2( 1;1) ex = 1 + x + x2 2! 0000003687 00000 n + ::: so: e = 1 + 1 + 1 2! x 2R cosx = 1 x2 2! 0000024470 00000 n + x3 3! N�Ma��n�� �@!��p�=2�a�a�9$;s���x�N�Q�b��}��'��u丷�a2���C.G"-Sl+ {k���a���9�z�Sa2G;]�fr��#����u�(��J��Y�5dM�QqY����J㘽�a��]f"d����>�4(�`N(�Z��4�,ͷG�"�k�S�sPjZ,���l.~��T�B���J)j���vp��`�� e�}E�&Żup�E�.W�0��Y���v��f�GK y���'��DCێQ����s�y��.���7k��F^5�f#_4. 0000023507 00000 n

0000014719 00000 n 0000108908 00000 n Appendix A: Taylor Series Expansion 221 In particular, it means that we only need to keep first-order terms and only one second-order term (dB×dB= dt), ignoring all other terms. stream The function f(x) = ex satis es f(n)(x) = ex for any integer n 1 and in particular f(n)(0) = 1 for all n and then the Maclaurin series of f(x) is f(x) = X1 n=0 xn n! Commonly Used Taylor Series series when is valid/true 1 1 x = 1 + x + x2 + x3 + x4 + ::: note this is the geometric series. 0000015405 00000 n To nd Taylor series for a function f(x), we must de-termine f(n)(a). 0000106715 00000 n 0000011732 00000 n %PDF-1.4 Math formulas and cheat sheet generator creator for Taylor and Maclaurin Series. + x4 4! 0000016519 00000 n

05/29/2011 1: ex = X1 n=0 1 n! 3 0 obj << For the following examples we will assume that all of the functions involved can be expanded into power series.

0000040642 00000 n We now recall the definition of nth order excision, from section 3 of [10]. 0000019439 00000 n

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In this section, we are going to use power series to represent and then to approximate general functions. 0000017955 00000 n Standard Taylor Series Math 126E.

trailer <<7F18CFF5C56A4CD48C7A5F105CC8CE05>]/Prev 134344/XRefStm 1973>> startxref 0 %%EOF 121 0 obj <>stream %PDF-1.3 0000014332 00000 n 0000002277 00000 n 0000034954 00000 n /Filter /FlateDecode Suppose we wish to approximate f(x0 + x;y0 + y) for x and y near zero. + 1 4! The Taylor series for the hyperbolic functions are closely related to those of the trigonometric functions. Example: sine function. �)/b��,��u7]��0��r�Ԛ�cs��X5�E�>��걂���ڈ���Lr�'ɷ�Ɛ� endstream endobj 120 0 obj <>/Filter/FlateDecode/Index[5 49]/Length 20/Size 54/Type/XRef/W[1 1 1]>>stream 0000106586 00000 n Cette feinte commence toujours par poser h := x a. x2n = 1 x2 2 + x 24 x6 720 +:::; x 2R 3: sinx = X1 n=0 ( n1) (2n+1)! stream We’ll see examples of this later in these notes. La table de TAYLOR définit la combinaison théorique idéale entre le TAC, le pH et le TH.

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