MTH301 Quiz 2 November 2025

Question:

What is the condition of the extreme value theorem?

1. A function must be differentiable
2. No conditions are necessary
3. A function must be continuous and differential
4. A function must be continuous on a closed interval

Copied: 11/24/2025, 10:25:26 AM

Question:

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�A�.� Ø5Üe�c�o�s�(Ø5ÜeØ5Üf�) �B�.� "�s�i�n�(Ø5ÜeØ5Üf�) �C�.� Ø5Üf�c�o�s�(Ø5ÜeØ5Üf�) �D�.� �c�o�s�(Ø5ÜeØ5Üf�) Copied: 11/24/2025, 10:25:42 AM

Question:

�T�h�e� �c�r�i�t�i�c�a�l� �p�o�i�n�t�s� �o�f� �t�h�e� �g�i�v�e�n� �f�u�n�c�t�i�o�n� �f�(�y�)�=�y�3"�5�y�2�+�3�y�+�5�w�h�e�r�e� �f�y�(�y�)�=�3�y�2"�1�0�y �_�_�_�_�_�_�_�_�_�_�_�.�T�h�e� �c�r�i�t�i�c�a�l� �p�o�i�n�t�s� �o�f� �t�h�e� �g�i�v�e�n� �f�u�n�c�t�i�o�n� �f�(�y�)�=�y�3"�5�y�2�+�3�y�+�5�w�h�e�r�e� ___________.\eqalign{

& {\text{The critical points of the given function }}f(y) = {y^3} - 5{y^2} + 3y + 5 \cr

& {\text{where }}{f_y}(y) = 3{y^2} - 10y + 3 = (3y - 1)(y - 3) {\text{are ___________.}} \cr} �A�.� �x�=�1�3�,"�3�x�=�1�3�,"�3�x� �=� �\�f�r�a�c�{�1�}�{�3�}�,� �-� �3 �B�.� �y�="�1�3�,"�3�y�="�1�3�,"�3�y� �=� �\�f�r�a�c�{�{� �-� �1�}�}�{�3�}�,� �-� �3 C. x=13,3x=13,3x = \frac{1}{3},3 �D�.� �y�="�1�3�,�3�y�="�1�3�,�3�y� �=� �\�f�r�a�c�{�{� �-� �1�}�}�{�3�}�,�3 Copied: 11/24/2025, 10:25:58 AM

Question:

�T�h�e� �e�x�p�r�e�s�s�i�o�n� "+�c�d"+�a�b�f�(�x�,�y�)�d�x�d�y"+�c�d"+�a�b�f�(�x�,�y�)�d�x�d�y \int\limits_c^{d} {\int\limits_a^{b} {f(x,\,y)\,\,dx\,dy} } is called --------- integral.

A. irregular B. iterated C. repeated D. iterated and repeated Copied: 11/24/2025, 10:26:43 AM

Question:

If f(x,y)is continuous on a rectangular �r�e�g�i�o�n� �a�<�x�<�b� �a�n�d� �c�<�y�<�d� �t�h�e�n� "+�a�b"+�c�d�f�(�x�,�y�)�d�x�d�y�w�i�l�l�b�e�.�.�.�.�.�.�."+�c�d"+�a�b�f�(�x�,�y�)�d�x�d�y�.�I�f �r�e�g�i�o�n� �a�<�x�<�b� �a�n�d� �c�<�y�<�d� �t�h�e�n� "+�a�b"+�c�d�f�(�x�,�y�)�d�x�d�y�w�i�l�l�b�e�.�.�.�.�.�.�."+�c�d"+�a�b�f�(�x�,�y�)�d�x�d�y�.�{�\ continuous on a rectangular region }}a < x < b{\text{ and }}c < y < d{\text{ then }}\int\limits_a^b {\int\limits_c^d {f(x,y)dxdy} } \;{\text{will}}\;{\text{be}}\;\;.......\int\limits_c^d {\int\limits_a^b {f(x,y)dxdy} } .

A. less or equal to

B. equal to C. greater or equal to D. not equal to Copied: 11/24/2025, 10:26:58 AM

Question:

�E�v�a�l�u�a�t�i�o�n� �o�f� "+�0�1"+�0�2�x�2�y�d�x�d�y"+�0�1"+�0�2�x�2�y�d�x�d�y�\�i�n�t�\�l�i�m�i�t�s�_�0�^�1� �{�\�i�n�t�\�l�i�m�i�t�s�_�0�^�2� �{�{�x

A. 2/32/32/3 B. 8/38/38/3 C. 1/31/31/3 D. 4/34/34/3 Copied: 11/24/2025, 10:27:14 AM

Question:

What does the Extreme Value Theorem state?

1. Every differentiable function has an absolute maximum and an absolute minimum.
2. Every continuous function has either an absolute maximum or an absolute minimum.
3. Every continuous function on a closed interval has an absolute maximum and an absolute minimum.
4. Every function has an absolute maximum and an absolute minimum.

Copied: 11/24/2025, 10:27:39 AM