Cálculo II - Atividade de Estudo II - 07/03/2016 - Engenharia de Produção - Unicesumar EAD

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CÁLCULO DIFERENCIAL E INTEGRAL II 
ATIVIDADE DE ESTUDO II - 07/03/2016 
UNICESUMAR EAD – ENGENHARIA DE PRODUÇÃO 
 1ª QUESTÃO 
 
� − 2��� + 3��3� + 1� = �� + 3 + �3� + 1 ; ������� 
����������� � �����: ��3� + 1� + ��� + 3��� + 3��3� + 1� = �3� + ��� + �� + ���� + 3��3� + 1� 
�3� + � = 2� + � = 0 → � 3� + � = 2−3� − 3� = 0 → � −2� = 2� + � = 0 → �� = −1� = 1 
�� − 2��� + 3��3� + 1� = �� + 3 + ��3� + 1�" ; #��������, ��#% �� + 3��3� + 1� %ã� '�����% �#�����% (�� �ã� %� �������. 
��� − 1��� + 1�" = �� + �� + 1 + ��� + 1�" ; �������, ��#% ���� �� + 1�"é �� '���� �#���� (�� %� ������ ����% �� �����#� � '���� � ��%�� �ú���� �� ,�-�% �� ��������. 
.�: %� � �����#����� '�%%� ��� + 1�/'#���#�: �� + �� + 1 + ��� + 1�" + 0�� + 1�/ , %����� �����#���, ��#�#������ + 1 �� ��������, ��é ��#�1#� � �������� ��#1#���. 
�2 − 1��� + 1�" = �� + ��� + 1�" ; #�������� ���'���� ����#���� �� #��� ���. 
2 − 3�� + 1��� + 2�" = �� + 1 + ��� + 1��� + 2� ; #��������, ��,��#� '#��� �� + 1 + ��� + 2� + ��� + 2�" 
 
 
 
2ª QUESTÃO 
 
3 3 �1 + 4�5����567
/
6 = 3 � + 2�"5]9:79:6�5
/
6 = 3 �1 + 25��5
/
6 = 5 + 5"];:6;:/ = 12 − 2 = 10 
 
 3ª QUESTÃO 
 
3<%��/��� ∙ ��%"���]�� = 3<%����� ∙ %��"��� ∙ ��%"���]�� → %��"��� = 1 − ��%²��� 
3?%����� ∙ ��%"��� ∙ @1 − ��%"���AB�� → � = cos��� → �� = − 1%����� �� 
3 F− %�����%����� ∙ �"�1 − �"�G �� = − 3��" − �H��� = − I13 �/ − 15 �KL + � = 15 ��%K��� − 13 ��%/��� + � 
 
 4ª QUESTÃO 
 
3<������]�� → � = ����� → �� = 1� ��; �, = ��� → 3 ��� = 12 �" = , 
� ∙ , − 3 , ∙ �� = 12 �" ln��� − O12 3 �
"
� ��P → 12 3 ��� = 12 ∙ 12 �² = 14 �² → 12 �" ln��� − 14 �² 
 
 
 
 
 
 
 
 
5ª QUESTÃO 
 
� − 56 = �; 5" = �"; <�0,0��1, 1�] → � = �", � = 0 �� � = 1, ������� 
�� − 56 = �"; 5" = �H; <�0,0��1, 1�] → �" = �H → �H − �" = 0, � = −1, � = 1 �� � = 0, #�������� 
��� − 56 = 1� ; 5" = 1�" ; <�0,0��1, 1�] → 1� = 1�" → � = 1 , #�������� 
�2 − 56 = 1 + √�; 5" = 3 + �3 ; �ã� %� ����� → 1 + √� = 3 + �3 → 3 + 3√� = 3 + � → 3√� = � 
→ 3√� − � = 0 → 9� − �" = 0, � = 0 �� � = 9, #�������� 
2 − 56 = %�����; 5" = cos��� ; %� ����� �� 3 �����%; %����� = cos��� � ���� � ∙ S + S4 , #�������� 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6ª QUESTÃO 
 
3 1�"√�" − 9 �� → � = TUVWX → �� = TUVWX ∙ YZ[X ∙ \X 
→ ]�" − 9 = ]�3 sec θ�" − 9 = ]9%��²` − 9 = ]9�%��"` − 1� 
→ %��²` − 1 = ���²` → ]9���²` = TYZ[X 
3 1�"√�" − 9 �� = 3 3%��` ∙ ���`9%��"` ∙ 3���` �` = 3 327%��` �` = 19 3 1%��` �` 
→ %��` = 1��%` → 1%��` = 11��%` = 1 ∙
��%`1 = WbUX 
19 3 1%��` �` = 19 3 ��%`�` = 19 %��` + � 
 
�1��� ,������� � �: 
→ %��` = 1��%` → ��%` = ��ℎ# → 1��%` = 1��ℎ# = 1 ∙
ℎ#�� 
� = 3%��` → %��` = �3 → ��%` = 3� , ���� � é � ℎ#������%�, � 3 � ������ ��d������, ���ã� ]�" − 9 é � ������ ���%��. 
→ %��` = ��ℎ# → %��` = √�
" − 9� 
e�f%�#��#���: 19 %��` + � → 19 √�
" − 9� + �, �� 19 g�² − 9� + � 
 
 
 
 
 
 
 
 
 
7ª QUESTÃO 
 
há ���% '����% �� ��%��,�� �%�� �����í�#�, ����%'������� � � �� '��çã� �� 5 � '�-���� � �é���� ��% �����%, �� ��#�#-���� � 'ó����� �� �é���� �� ������% �#�í���#��%, �� �á1#�� 73 �� ���%�#��. lã� %�# ��� (�� � ���'�%%�� ���'��#� ��#�#-�� � ��#��#��, (�� '�# �����% ����#����� ,�1������ �� ���%�#��, ��% �� ,�� �����%���� �% ���% '����%. 
� − mé���� ��% �����%, ��� � �� '��çã� �� 5 
e� 56 = �/���ã� � = ]5n , � � 'ó����� ���� � ,����� %��á 
3 S<@'���A" − �1����²]��op → 3 S@]5n A"�5
q
7 = 3 S5
"/�5q7 =
35 S5K/]7q = 35 S ]8Kn = 
35 S √32768n = 32S ∙ 35 = 965 S �. ,. 
 
� − mé���� ��% ������% �#�í���#��% 
l�%��, ���� �f��� � #����%��çã� ����� 56 = �/� 5" = 8 ����% �� '�-�� �/ = 8, � �f����% � = 2, ���ã� � #����,��� �� #���1��çã� %��á <0, 2]. t����f� − %� ���fé� (�� � 1�á'#�� �� 56�%�á �f�#�� �� 1�á'#�� �� 5". � 'ó����� ���fé� é �� ����� �#'������ 
2S 3 �<'��� − 1���]��op → 2S 3 ��8 − �/���
"
7 = 2S 3 8� − �H��
"
7 = 8S�" −
25 S�K]7" = 
32S − 645 S = 160 − 645 S = 965 S �. ,. 
 
 
 
 
 8ª QUESTÃO 
 
�% #����#����% ��#�#-���% �� �é��#�� �� %�f%�#��#çã� ��#1����é��#�� %ã� 
→ %��²` + ��%²` = 1 → 1 + ���²` = %��²` 
 
 9ª QUESTÃO 
 
4��� − 1�"�� + 1� = �� − 1 + ��� − 1�" + �� + 1 = ���
" − 1� + ��� + 1� + ���" − 2� + 1��� − 1�"�� + 1� = 
�"�� + �� + ��� − 2�� + �−� + � + ���� − 1�"�� + 1� = u
� + � = 0� − 2� = 4−� + � + � = 0 →
� + � = 0−� + � + � = 0� + 2� = 0 → 
u � + � = 0� − 2� = 4� + 2� = 0 →
� − 2� = 4−� − 2� = 0−4� = 4 = v = w, x = y, z = −w 
 
 
 
 
 
 10ª QUESTÃO 
 
� + 25 − 2 = 0 → - = � + 25; 56 = �; 5" = �H → � = �H → �H − � = 0, � = 0 �� � = 1 
e� � = 12 , 56 = 12 , 5" = 116 ; � 1�á'#�� �� 56�%�á ��#�� �� 1�á'#�� �� 5" �� #����,��� <0, 1] 
3 3 �� + 25��5��99{
6
7 = 3 �5 + 5"]|}~{
|}~ ��67 = 3 �2�" − �K − �q���
6
7 =
23 �/ − 16 � − 19 �€]9:79:6 = 
23 − 16 − 19 = 12 − 3 − 218 = 718 �. ,. 
 
 
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