1 0 obj << Mechanical M – 1 Batch – C 2. Rather, they represent forms that arise when trying to evaluate certain limits. We can force a common denominator: 1 1 e u 1 u = u 1 + e u u(1 e u): As u !0+, the right-hand-side is now a \0=0" form and can be treated using l’H^opital’s rule. endobj 18.01 Calculus Jason Starr Due by 2:00pm sharp Fall 2005 Friday, Dec. 9, 2005 Solution to (b) By plugging in x = π/2, we see that the limit becomes ”1∞”, which IS an indeterminate form. �8J�l���͊:�'i;��,���%���x��0�yVٛh! Understanding their indeterminate forms is crucial. Before we can use l’Hopital’s rule we must bring the expression into an indeterminate form of either of the two types: 0 0 or 1 1. ~E3���Dvԅ�˯�'1�{R��a6P�ji-�,^O'�m������,3�py��U!�l6W4�I�����%(g✓"���nvj�6�G��_Y���Fo�(�Thg�V�ՇO����l�1�)5d���À5{/3{��£>�o:ޞXa&���if�N� ��t�'�b?�&O��oC=��z�WUBY=!�. f4� View Worksheet-6-Solutions.pdf from MATH 1202310 at Oak Ridge High School. �. >> Sa�X$\֏���:,�d�z�O����:�6��㭔� ��͂5��-�ȏe�t��p�� ^tT��6^])�* Indeterminate Differences Get an indeterminate of the form ∞−∞ (this is not necessarily zero!). • It is indeterminate because, if lim x→a f(x) = lim x→a g(x) = 0, then lim x→a f(x) g(x) might equal any number or even fail to exist! 1 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the … to exist! /MediaBox [0 0 612 792] stream /Length 1412 �K�;�)�hr�yBX�gܜM6��O�V�_U=ؑ\���y����1��0�����q5 �N�ٞ���}g�3����wn**T�j`�$��L(?1��&�5���&I�� ��̃h%��V���5T��SҪ�ᮙ��*��WZ��6d9d���rǦ�ҍ�A\��:M6dM6� ��!�{�{"����'=p�>��`4��V�&�ZT� V:+���Q�)�(�aN�yC��t�07�&hR�kIpo�V�0��k�,>Ib�d��B>#;}���g3�� �QN��f endstream �>&*��SOr�Tq�EO�"�+�4&���X��`�fUJ���F>ȃ�ݸ�;�R� %PDF-1.4 State each limit’s indeterminate form "���u�s�U�����U�~���/��r��>[G����w���Nj7/^�n�K$�q������H��b]��:J3O�����Lg9ł�s��\o��`�0���*n�w�e1����A]1�Ĥ�H�8�Vg [X�m���qf���l��$&yCL1kle�w=�)�*�q�R���E�=If�ӑc��# ���.kMҠ�+�[Q����Z1�s4sDX�>�Ւz���9�z���C̢"��?�N4�q#0,#s���SGR[f���neyWL�d!�Z���>�]�R�u�W�:��%���Wg�>��k��1�.gg�?�� <> ]�s%�P%�fTR0�L���z��l�4��nqw�|�KW��ϗ� ����x��o6�y�^�n��f�]���]��m�������`��ן���(#��)�J &��6BktH��2o�h���pST� �F�K#>S���7ߵz�@�1e\'�s��L�Ti&��b��d���02���X3{w=�X�(�׌�-�'&��r;���7x���LYW<6��B�"�)����&ٍ81m}a�d�\���iOe�a^I�J��R����V$Aj%�b�;d���6����P��q����WEO��V@i�ۯⵁ�"Q���z!����F��bRF+�`�D���F�nثR�X� �x�A��mL�1�x�������. �� G��M���^O�z^�ե����Js^������a��-����ܫr�>�? Examples with detailed solutions and exercises that solves limits questions related to indeterminate forms such as : Theorem A second version of L'Hopital's rule allows us to replace the limit problem stream %PDF-1.4 While an indeterminate form may not change your life, it can provide the means for further understanding of broader calculus concepts and rules. Next we realize why these are indeterminate forms and then understand how to use L’Hôpital’s rule in these cases. /Filter /FlateDecode %���� To see that the exponent forms are indeterminate note that /Type /Page Worksheet 6: (4.4-5.2) Solutions Indeterminate Forms and L’Hospital’s Rule 1. By Ketul Vaidya(15BEMEG061) Prashant Ranade(15BEMEG062) Aakash Singh(15BEMEG063) Aditya(15BEMEG064) Swapnil Bodke(15BEMEG065) F.Y. Lecture 7 : Indeterminate Forms Recall that we calculated the following limit using geometry in Calculus 1: lim x!0 sinx x = 1: De nition An indeterminate form of the type 0 0 is a limit of a quotient where both numerator and denominator approach 0. /Parent 13 0 R '������)׆�*�����������>�����&q�;���Nw���f�1��g-�_D]�n�"�1�k�^���R~Dcb:S�x��� stream Such a problem is known as an indeterminate form 0 0. ߽)8S�E�YA�ظ-ޝ�VbX�;��0�A�IG�dm�t������pQ" NK�jE��ί&��j6��7��f5�E�MD����)P��xY |���H8� ?+&��8�y`����l�y&�h: ���⤙�i&M�s�b�� �[�ժ��S�~cT�~�����x�x�cΗ��z��vx�f�]�* �g���{^Y��#��{;@h�*@Z-���5�����F��{��1�tOC�� /Contents 3 0 R B.E. /ProcSet [ /PDF /Text ] /Resources 1 0 R ~�-,1F��U�����1|��G�7 �B�#xxq^�j9��V� >> endobj �ޟ��p/h�� ?���u��� /Font << /F23 4 0 R /F15 5 0 R /F27 6 0 R /F30 7 0 R /F24 8 0 R /F26 9 0 R /F29 10 0 R /F28 11 0 R /F25 12 0 R >> Solution: Here we have an indeterminate form of the type "(11 )" as we deduce from the fact that lim x!1 + 1 xe1 = +1and lim x!1 1 (1) 1 = +1. >> The term was originally introduced by Cauchy’s student Moigno in the middle of the 19th century.