1) Find the limit of several functions as x approaches various values. 2) Complete a calculus test covering chapter 1 on limits and continuity. 3) The test contains 12 problems evaluating limits of functions both analytically and graphically.

1. Name__________________________
CALCULUS BC TEST #2 1ST SIX WEEKS
9/9/10
Chapter 1: Limits and Continuity
Find the limit of the following functions, if it exists. An analytical solution is expected.
x 2 −4 x −12 tan θ
1) lim 2) lim
x→ 2
− x +2 θ→
π θ
4
x +4
3) lim
x →2 ( x − 2) 2 4) ( x + ∆x) 2 − 4( x + ∆x ) + 1 − ( x 2 − 4 x + 1)
lim
∆x →0 ∆x
tan 2 x x 2 −9
5) lim
x→0 x
6) lim
x→ −
3 x −3
3−x x <2
7) f ( x) =  2 Find lim f ( x ).
x − 3 x >2
x→2
 1 x<0


8) Use g ( x) =  1 − x 2 0 ≤ x ≤1 to evaluate the following:
 2x −1 x >1


a) g(0) b) g(1)
c) lim g ( x) d) lim g ( x )
x →0 x →1
e) Describe the continuity of g (x) x y
Use the tables to find: 2.9 1 / (-x10
-
2.99 3- 100
)
2.999 - 1000
3 undef
3.001 1000
3.01 100
3.1 10

2. 9) a) lim f ( x )
x→ +
3
b) lim f ( x )
x→ −
3
c) Describe the graph of f(x) at x = 3.
x y
10) a) lim f ( x ) 6.1 ( x- . 1
10
6 ) 10 .+4
( x 01
+
x→6
6.01
) / ( x-
6.001 10 . 001
lim f ( x ) 6)
b) x→ −
6 6 undef
5.999 9 . 999
c) Describe the graph of f(x) at x=6.
5.99 9 . 99
5.9 9. 9
11)
12.