Download - AP Calculus TEST: 1.1-1.4 No Calculator
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AP Calculus TEST: 1.1-1.4 No Calculator
Part I: Multiple Choice—write the CAPITAL LETTER in the blank to theleft of the problem number.
Use the graph of the function ( )g x shown at right to answer question 1.
_____ 1. � �� � � �2
3 1 1lim lim 3 ( ) limx x x
g g x g x g x� � ��� � ��
� � � =
(A) 6 (B) 7 (C) 8 (D) DNE
_____ 2.2
7
2 13 7lim7x
x xx�
� ��
�(A) � (B) 0 (C) 2 (D) 15
_____ 3. If 7 12csc ( ) ln 1 2P x xx x� � � � � � �� � � �
� � � �, for all x in an interval containing 6x � , then
6lim ( )xP x
��
(A) 1� (B) 2� (C) 2 33
� (D) not enough information is given
_____ 4.5 4
10 8
3 9 1lim9 4x
x x
x x���
� � ��
� �
(A) 1� (B) 1 (C) 13
� (D) 13
_____ 5. � �� �� �� �6
5 7lim
5 6x
x xx x��
� ��
� �
(A) �� (B) � (D) 1 (E) 1�
_____ 6. If � �
2 2 , 12, 13 5 , 1
ax b xf x x
ax b x
� � ��
� ��� � ��
is continuous at 1x � for particular values of real numbers a and b, what is
the value of ab
?
(A) 211
(B) 10 (C) 2011
(D) no such values of a and b exist
_____ 7. If � �f x is continuous for all x in the interval � ,a b , then at any point � �,c a b , which of thefollowing must be true?
(A) � � � �limx cf x f c
�� (B) � � 0f c � (C) � � � � � �f c f b f a� � (D) � � � � � �f a f c f b
_____ 8. Evaluate4
5 3lim4x
xx��
� ��
�
(A) 1 (B) 16
(C) 16
� (D) 6�
Part II: Free Response: Answer all questions in the rectangle provided for each problem. Show all steps, useproper notation, and write legibly.
� �
3 2
2
2
2 3 , 33 4 1
3 1, 3 21
2 , 2 2
1 3 , 2 4
5 2 , 43 2
x
x
x x xx xx x xx
f x xxx x
x�
�
� � �� ��
� ��� � �� � � �
�����
� � ���� � �
��� �� ��
��9. For the function given above, find the following.
(a) � �3
limx
f x�
�
(b) � �0
limx
f x��
�
(c) � �limx
f x��
�
(d) � �limx
f x���
�
(e) Using the 3-step definition of continuity, discuss the continuity of � �f x at 2x � � .
(f) Using the 3-step definition of continuity, discuss the continuity of � �f x at 2x � .