Name_________________________________________ Date______________________ Period___________

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 � .