}~�ߛ��p��E�B5�I0���̻l���=��v��&���?%�H�ɔ_�Z�$$��Q$��S�"gEt���t����uY����� ��j�ьV� Integrals 5. x��][s�q��c���Ƴ��f�U��HqJ.ɉ%�y�]) � P� ��A~�K�`��k�]���h� formula to convert into an integral involving trig functions. J����� ���X/i�1ֈ�3�x������k�h��@��L̔�FP��7��f���tl �$�0FM:9�O4�:�'吼pK����t9gzE�U��s���վ�%{�OO}3�e���"����%��x=n�m�E�vY��3z��;�. � ����c$�(Г��R�z���$$R�&~�~)?�;���)"9�LD. Applications of Differentiation 4. *�u�٠��_16w&����5�Q�gGkc���c��E��zM�/z�ͤ��M�����l.�f1���1{�_����-4�/cX����$1��*� Introduction. %�쏢 !������!H�6 b��&�L�]�$&�{#@�iPp)�x�%�N}"����N;3�Nf�� %PDF-1.4 Volumes of Revolution : The two main formulas are V A x dx=∫ ( ) and V A y dy=∫ ( ). @�C9�%>�3>fpzSi�S�>�����N�-q�.O}��ԇ��q9N���a��2�dQ�� l#H���(�xx��P��"�;�����-o��?u ��������y,�� �������4���c�z���r*Ia����ŏ_���������ȿy ����2{�$��S�?͞�� H�0H��5�T�q8=�m C�D���\ }���]�����G ��+X�T�!v�׃ |h\(�;����b���G�Ο�Ĺ���~Pyȣh�o�@4���o!q"��C��fm�Y���~H>�G�������'�ݹ��kڶv2��n�Ð�^���@? %PDF-1.5 8ER��ҊdK�°y)p�P[Zg�qP*��"��+e�G�_��PFj #!#)������f�C2ڷ4e�Y�DDPّPjk�^�8�|������ͧW������S�GȨ��׹ݣu����������H!�i��s�|�.�(�\�)��$�G�8�\r.7�47+[0�'ALYn��]� �ͺ����Ǣ����K]�u���`�u�dY^m�����lIa�FNw*�*��C�� �؞66�ݢ�؀����Og��\N���^Ypp�ca5����D�?��3z���8��f�nm����6�1�pG��z_�6���s��}�_����P /��bҞ�����Ӈ"Ot��^�+�͖��E�H���]�X����7а*jT����I���!��� �6׾�2^� Ϫ$awj����8���0,�����+_�:�;;���C��]F��[�z���S�D���ta�H�i %PDF-1.3 <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> ���a'Go��Cx��K�H4F��:��5,C�(4��N���e?��c|�W��D��χ8+m��Z���&N�y�8��5�ϨX���CG�l��?,WҪŨѣ��ɰE�qR�u�g��vd��Խ�������ad��z���Y��Kr����ղh��ۯ! #I�za㑊O�� +x/�$�$W�u,���Pk����(͌�^$�gEY��df?=nK��b鋫�g�;�����g�T�T�d�_\�4���e�7{����ѯ��m�zgc��8�/�wW�Y��[:�*=AJѫ� ��l�gf�ݥ��q�{����V�֕׽�xѝ2���n��,��g*;����{�Ԙ,���'���' Ļ^�][�e~�ʁ}�p����3��E?b>]��j!|��~�����v q��ŏ�� Basic Properties and Formulas If fx( ) and gx( ) are differentiable functions (the derivative exists), c and n are any real numbers, 1. 16 0 obj It is not comprehensive, and CBC MATHEMATICS MATH 2412-PreCalculus Exam Formula Sheets CBC Mathematics 2019Fall Rational Zeros Theorem: for polynomial function ( T)= T + −1 T −1+⋯+ 1 T1+ 0 having degree of at least 1 and integer coefficients with ≠0, 0≠0 • If << /Length 5 0 R /Filter /FlateDecode >> endobj ��{:�탇�z��? BASIC CALCULUS REFRESHER Ismor Fischer, Ph.D. Dept. stream Level 3 Calculus, 2016 9.30 a.m. Wednesday 23 November 2016 FORMULAE AND TABLES BOOKLET for 91577, 91578 and 91579 Refer to this booklet to answer the questions in your Question and Answer booklets. 16 x2 49 x2 dx ∫ − 22 x = ⇒ =33sinθ dx dcosθθ 49− x2=−= =4 4sin 4cos 2cos22θ θθ Recall xx2= . If f(x) is a rational function given by ( )= ( )),such that ( ) and ( have no common factors, and c … 4 0 obj Math 116 : Calculus II Formulas to Remember Integration Formulas ∫ x n dx = x n+1 /(n+1) if n+1 ≠ 0 ∫1 / x dx = ln |x| ∫ e nx dx = e nx /n if n ≠ 0 Derivative Formulas : d/dx (x n) = nx n-1; d/dx (ln x) = 1/ x d/dx (e mx) = me mx. "�H//ZYU��q+�)��%mT7�����`��S��ۻ,��nf)�ǚ��M�M�J{�7:����!�0�BI�[��i�`���^��4�>7��^h�B/��J68c� F:& J��?��I9�_�F_�ڨ��;W�K��g�����L�?��$�;>�ܼ͑:��w�_�Fzk6$����������"7X �0����?��U��/�3���Hm76 %���� <>>> This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in Mathematics, Statistics, Engineering, Pharmacy, etc. ����1� � s�g��c̔1�Qk�gIY!��Af�]Vt�_�:�>TP��F�$,����f4�Kx��wu/���,�`.�jө��d]�ҙѪ�pH�2S���XN��p�W͸3}�պ]���;�Ǯˇ�"�ϳퟱ�Tx������-l�C3���Nu *���p�M�fY�ΪQ�%lj�kҤ��2���+Ǒ�e���(}Y���|. ҃s�������L��ۍ������G����|��Q*�|����ۣ0j�'p��r��hQ*����c�����HG�6V�?_=�~5��E���7Z�����0#��^f"x�=vft�z�}1H1j���!�A��Y)a����"���1�:}��,u�/� Z� #W}�^uq���^F�F{z���yo����h����k0��ЁϘ��$��>Kޠ�"OLL�쿳��!0�:���>h��7KZ~1���WG���H6s|a�/������"��H�X����zRV��}Շ�h�ةWK�1��-W W*��A�v��d��1jg�������~1`�I����)���[3���66�J�?�. Here is some general information about each method of computing and some examples. Calculus I Formulas MAC 2311 1. (f–g)¢ =–f¢¢()xgx() 3. ()0 d c dx = 6. d (xnn) nx 1 dx =-– Power Rule 7. �X�dw��y�&�!�e��:��jyIQ�X���Eab�a>��vwW�2Cj�,��0>^��c��e�E�dً�X���elp���T��`��`��{ �i�i���i��H����juݡ-ޣ���f�. (fg)¢ =+f¢¢gfg – Product Rule 4. 1 0 obj AP Calculus Formula List Math by Mr. Mueller Page 6 of 6 ( ) ( ) ( ) ( ) ( ) 2 2 2 Polar Coordinates and Graphs: For : cos , sin , , tan cos ' sin cos 'sin Slope of a polar curve: sin ' cos sin 'cos Area inside a polar curve y r f x r y r r x y x dy dy d r rf f dx dx d f f r r Applications of Integration Professor: Dr. Mohammad Shakil C0-Author: Jeongmin Correa Mathematics Department <> Basic Properties and Formulas If fx and g x are differentiable functions (the derivative exists), c and n are any real numbers, 1. cf cf x x��\[s۸~��= ���n7�fg��nܧ���ؚ��D�������g��d2�)��p�w. Assume that f(x,y) is a nonnegative on R. Then the volume under the