The document contains 14 sample calculus problems involving limits, continuity, and other calculus concepts. It provides examples of limits as expressions approach specific values, determining if functions are continuous or discontinuous at points, and evaluating limits of indeterminate forms. The problems are presented without solutions to be used for practice and review. Helpful hints are also given, such as never leaving standardized test problems blank since there is no penalty for guessing.

1. Calculus Warm Up
Sample Problem #1I
The absolute value of the
difference between r + 7 and r
– 4 is:
A) 3 B) 5 C) 7
D) 9 E) 11

2. Sample Problem #2I
The ratio of girls to boys in Mr.
Quadwad’s homeroom is 2/3. Each
of the following could be the total
number of students in the
homeroom except:
A) 15 B) 24 C) 25
D) 30 E) 60

3. Sample Problem #3I
30°
6
6
6
30°
Note: Figure not drawn to scale.
What is the perimeter of the figure
above?
A) 24 B) 25 C) 28 D) 30 E) 36

4. Sample Problem #4I
Find region in the first
quadrant bounded by the axes
and the line 3x + 4y = 12 has
an area of how many square
units?
A) 4 B) 6 C) 8 D) 10 E) 12

5. Sample Problem #5I
The price of an HDTV was first
decreased 20% and then increased 20%
of the new price. The current price is
now:
A) the same as the original
B) 2% more than the original
C) 2% less than the original
D) 4% more than the original
E) 4% less than the original

6. Helpful hint #4:
SPR’s have no
penalty for guessing so
NEVER leave them blank!

7. Calculus Drill
•1. Find the limit
lim
x 0
|x|
x
lim
x 2
|x–2|
x – 2

8. HW Review
• http://college.cengage.com/mathematics/blackboard/

9. Review
•1. Find the limit!
lim x
+
1 x
®
3

10. • 2. Continuous /
Discontinuous? Removable or
Not
2
1
1
x
lim x
®- x
1 -
+

11. Review
•3. Find the limit!
lim(3 x 3 - 2 x
2
+
4) x
®
1

12. • 4. Continuous /
Discontinuous? Removable or
Not
f ( x ) x
+
2
=
x +
2

13. Review
•5. Find the limit!
2
+
lim 1 x
1
x
®- x

14. •6. Find the limit
( ) 27
lim
x c
®
lim
lim
lim
( ) 3
( )
3
2
x c
®
( ) ( )
18
x c
®
( ) [ ( )]
x c
f x
a f x
b f x
c f x
®
=

15. Review
•7. Find the limit!
3
+ -
-
1 2
x
lim x
® x
3

16. • 8. Continuous /
Discontinuous? Removable or
Not
2 2
4 1 2 ( ) x x
x x x f x ì - £ ü
= í î 2
- + ý þ

17. Review
•9. Find the limit!
2 2
+ D -
D
lim( ) x
0
x x x
D ® x

18. Review
•10. Find the limit!
æ 2
+ ö
ç ¸ è - ø
1
1
x
lim x
® - 1/( x
1)

19. Review
•11. Find the limit!
0
1 1
x
lim 4 4 x
® x
-
+

20. • 12. Continuous /
Discontinuous? Removable or
Not
lim3 2
x
9 x
®- x +

21. Review
•13. Find the limit!
2
2
1
1
x
lim x
®- x
1 +
-

22. Review
•14. Find the limit!
lim 1 1 x® x
2
0
æ + ö çè ø¸