The limit form af, for 11a [1ex] Condensed: The “form” 0 0 is indeterminate. 4. ∞ ∞0 00 1∞ ∞ −∞ Remember that ∞ is not a real, honest number, but a shorthand for a limiting process. The limit forms a rf, for any number a, and bounded rf result in a limit of 0. This first is a 0/0 indeterminate form, but we can’t factor this one. to exist! This is where the subject of this section comes into play. I5D&�*JY�is,�$q���/_oTeaBdK�7pY�Bi��js�e�����v� 2. /Length 1995 h�b``�c``����� }�A�����,,*��x8/v87� l;� R"S�s���f�#�O�p��`�h(�`�h�h�h��@����b��
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• 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! h�bbd```b``����`v�d��L�fN0��fO���"���S �~+Xd 522 0 obj
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These indeterminate forms have many types that all require di erent techniques that will be broken down in the sections that follow. stream 1.2 Other Indeterminate Forms Indeterminate Forms Indeterminate Forms • The most basic indeterminate form is 0 0. The second is an \({\infty }/{\infty }\;\) indeterminate form, but we can’t just factor an \({x^2}\)out of the numerator. /Filter /FlateDecode ; ��Oف�,f;��U�;`E.�.H.9#\� w��w)��Ѕ��r`�iBI�����!��,���6���L�.i��ޣ>>��@ҝ�dתK|���'H��:��q���K'��$�?�*id�R�x�(���ӐL�5q��S��8B��1�� �]��s"���/@JQ���q�-����ϗ�kڛ� �g�k-s�_a��>p�O%FB@���Xe %���� 596 0 obj
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Determinate Limit Forms: Assuming that the functions involved in the limit are defined: 1. The limit form frf results in a limit of 0. 572 0 obj
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x��Y�n�F}�W�O��j��K�>$@��h�1Ї��M�Dd�!�:�����Z�+ٹ���"���3g�̬^��|�#S��QǪ��J��pC�ķ�����W+�ӟK!D͘�b���Ms�k��@֒�(��v����-�9�����d��.����o?��'?���?a�����v�h�r~s��?����_* %PDF-1.4 unpredictable limit forms are called indeterminate. 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. Indeterminate Form of the Type 0⋅∞ Indeterminate forms of the type 0⋅∞ can sometimes be evaluated by rewriting the product as a quotient, and then applying L’Hospital’s Rule for the indeterminate forms of … A5��]E���J��HF��"ZK�2`��'^p�#��E;N��ܝ$�R�;顡 �}4. �HC#݀�_�u��@d\�J�[�(�?�Xj��`ځ�v�\��xm�쇂�%v8V�o. h�Ė�n�H�_�/g.�}>I�HN2��4ɮb�f$��Y��0���oU6>;s�