Calc AB Chapter 1 Test Review
• Know the notation for limits
lim f ( x )
x c
• Know the difference between an infinite limit and a limit at
infinity
• Know terms from the notebook quiz and memorize quiz
• Know the three conditions to show that a function is
continuous
• Know the three ways to find a limit
• Numerically
• Graphically
• Analytically
Find Limits
1) Graphically
f ( 2) 
lim f ( x )
x 2
Find Limits
2) Numerically
x
0.9
0.99
0.999
f(x) -0.05 -0.0005 -0.00005
x
1.001
1.01
1.1
f(x) 0.00005 0.0005 0.05
lim f ( x )
x1
Remember your limit Properties
3)
If
3
lim f ( x) 
x c
4
Find
lim [ f ( x)  g ( x)]
x c
and
9
lim g ( x) 
x c
4
Techniques
x2  x  2
4) lim
x  2
x2
5) lim
x 0
x9 3
x
Absolute Value limits
x 1
6) lim
x 1 2 x  2
x 1
lim
x 1 ( 2 x  2)
x 1
lim
x 1  ( 2 x  2)
More Limits
7) lim
x 2
8)
2x  3
1  cos ( x)
lim
x 0
x
2
Infinite Limits & limits at ∞
1
9) lim
x0 x
10)
7 x 3  x 2  2x
x   3x 3  5 x
lim
Infinite Limits & V.A.
x  x2
f ( x)  2
x  x6
2
11) Find the asymptote(s) of
Limits @ Infinity & H.A.
12)
lim
x 
4x2 1
x
13) Find the horizontal asymptote of
2
x
f ( x) 

x3 x 2
Know Continuity Conditions
Where is the function not continuous.
14)
x4
f ( x)  2
x x2
discontinuous
2

x
x2
15) Is
, x2

f ( x)   x  2
1,
x2

continuous at 2?
Use 3 Conditions
Intermediate Value Theorem
16) Is there a value of c in the interval [-2,-1] such
that f (c)  1 for the function f ( x)  x 4  2 x3  3x  4
If there is, then find c, if the theorem does not
guarantee a c-value, tell why.
Discontinuities?
f (2) 
f (1) 
Homework
Page 91 # 3, 12, 15, 17, 21, 23, 29, 35,37,
55, 57, 60, 63, 66, 67 and 71
Chapter 1 review worksheet