ACOW LIMITS AND CONTINUITY MODULE
Updated 5/28/2016
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Activity B2 – Finding Limits at a Point Algebraically (Indeterminate Form part 1)
In activity B1 you found lim f ( x ) by evaluating f (a ) . In all of the examples and
xa
exercises in activity B1, f (a ) was a real number. In general, however, f (a ) does not
always yield a real number. Often it will yield an expression that has an indeterminate
c
form of
(where c is a real number). In this activity we will discuss the indeterminate
0
form when c  0 and activity B3 will discuss the indeterminate form when c  0 .
When f (a ) yields the indeterminate form
0
, we must use one of the algebraic
0
techniques(RS2) shown at right.
2 x2  9 x  5
.
x 5
x 5
1. Find lim
x2  6 x  5
.
x 1 x 2  4 x  3
2. Find lim
3. Given f ( x)  x 2 find lim
h 0
f (3  h)  f (3)
.
h
4. Given f ( x)  x  4 find lim
h 0
5. Find lim
x 4
6. Find lim
x 2
f (2  h)  f (2)
.
h
x 2
.
x4
x2
.
x  11  3
7. Given f ( x)  x , find lim
h 0
f (5  h)  f (5)
.
h
8. Given f ( x)  x  1 , find lim
h 0
f (1  h)  f (1)
.
h