applications of differentiation in real life examples pdf

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1 0 obj %PDF-1.5 endobj Calculus is usually divided up into two parts, integration and differentiation. endobj 0000003391 00000 n As always word problems pose extra troubles as the interpretation of the problem and invention of needed variables are themselves conceptually <> At time t 0, a beaker contains 2 grams of salt dissolved in 5 ounces of water. 3 0 obj For example, cylindrical food … 4 0 obj At time t 0, water is being added at 10 ounces/min and salt is being added at 3 grams/min. 0000001723 00000 n �,��kD����������I@{���|� .�@E{�w0�?��r�G�T�&V �/ϰ>�^!�t�g������ZT9��J\$9�&erz �,��r Y�dP�2''f���[�����V��. 0000002711 00000 n 147 0 obj<>stream 0000000016 00000 n endobj 0000001343 00000 n For example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration. endobj <> 3 0 obj Applications of derivatives (in real life!) y = f(x), then the proportional ∆ x = y. dx dy 1 = dx d (ln y ) Take logs and differentiate to find proportional changes in variables <> Peyam Ryan Tabrizian Friday, October 11th, 2013 Chemistry Problem 1 [That should look familiar!] ANTIDERIVATIVES If f(x) = - cos x, then F’(x) = sin x. Differentiation and integration can help us solve many types of real-world problems. 0000002933 00000 n 2 0 obj %���� stream <>>> How fast is the concentration of salt Each is the reverse process of the other. endobj We use the derivative to determine the maximum and minimum values of particular functions (e.g. xref Application III: Differentiation of Natural Logs to find Proportional Changes The derivative of log(f(x)) ≡ f’(x)/ f(x), or the proportional change in the variable x i.e. This tutorial uses the principle of learning by example. startxref So, an antiderivative of sin x is - cos x. 145 13 stream 0000002195 00000 n 2 0 obj 0000001427 00000 n %���� Example 1 . 0000001687 00000 n Optimization is the application of calculus-based graphical analysis to particular physical examples. x���Mk�0����B˖?��&M�X?�v(;���ԍu��\$ݚ, ��k=z%C���\$Z%y Differentiation has applications to nearly all quantitative disciplines. <>/ExtGState<>/XObject<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Economics, and General Applications 2.6 Marginals and Differentials 2.7 Elasticity of Demand 2.8 Implicit Differentiation and Related Rates Applications of 2 Differentiation Where It’s Used Minimizing Cost: Minimizing cost is a common goal in manufacturing. 145 0 obj<> endobj engineering. <>/Font<>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> |:�y����q��s�BpFpP��z�������WùFN-�i�{O��U� ``%b��0�ߞrD��"��&�T�\$K���@fT�����c��+5�t�D�M2% �3�PDL�����,i��K�PwY�K�X��I3t/�8��/s"�R�JZ�XAq�n�%�!���%�r��_�vK�;�mH��1Of��A�o�{�*�d� ͳl��2��|[��(|o��*K��GŲ�w��@C��[��0�k�jy��aD*{Y�>9�Tmm�� )��f APPLICATIONS OF DIFFERENTIATION . 3 Applications of Di erential Equations Di erential equations are absolutely fundamental to modern science and engineering. 5 0 obj 0000001800 00000 n The approach is practical rather than purely mathematical and may be too simple for those who prefer pure maths. Calculus (differentiation and integration) was developed to improve this understanding. endobj 0000001561 00000 n stream %PDF-1.5 <<0dd43d166263264e8934c4070b3b2fcd>]>> trailer 0 %PDF-1.4 %���� INTRODUCTION . A physicist who knows the velocity of a particle might wish to know its position at a given time. <> <> Integration is covered in tutorial 1. endobj 0000003619 00000 n %%EOF endstream ). <>>> Integral Calculus with Applications to the Life Sciences Leah Edelstein-Keshet Mathematics Department, University of British Columbia, ... 1.7 Application of geometric series to the branching structure of the lungs18 ... 3.6 Examples: Computing areas with the Fundamental Theorem of Calculus56 x��[�rܺ}w��O�LJ���K*�*[�m%�Kl���n(����lR��ߧ�p�`0�R.���X�O�^ ��޷�}Q��8ݶE�������v����]u��Xԛ����?���y{�����E\$R��,�2&�4�2҂���/��;�y�µKF��vo�_�8�Y� ����X8��G)��D�v��f￥lѼ|�����f�f�J�^�_ə�9��4����+���K��:��Cz��r�����?\�7W���d�z�������jT��|����x03��a�ҍ�UąO��L���Y Ϭ�\$��YE�E:N�7U����_a��U���O3���nj>�b�"WY錥ZD���'LF ���w�di�����,�biZ��{�#��W"�� ��`ԁ��b602���(V#���#X�E�dA�ˏ���u�ٶ�v}��q�Nie��,J3E������T�-�\$V@���L����g�űq�t�oN�. We have to find critical points then characterize them as minima or maxima depending on the problem. 0000000556 00000 n 4 0 obj cost, strength, amount of material used in a building, profit, loss, etc. 1 0 obj x�b```f``j ���|��� ���� JFIF H H ��RExif MM * b j( 1 r2 ��i � � H H Adobe Photoshop 7.0 2006:11:22 16:05:16 � �� � � X ( \$ &.