ACOW LIMITS AND CONTINUITY MODULE
Updated 5/28/2016
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Activity B3 – Finding Limits at a Point Algebraically (Indeterminate Form part 2)
To find lim f ( x ) we would first evaluate f (a ) . If f (a ) yields the indeterminate form
xa
c
,where c  0 , then the limit is either infinite or does not exist. Generally, the
0
c
indeterminate form ,where c  0 , arises because a vertical asymptote exists at x = a.
0
Therefore the function’s values will either:
1. increase without bound on both sides of x  a (i.e. the limit is ∞).
2. decrease without bound on both sides of x  a (i.e. the limit is –∞).
3. increase without bound on one side of x  a and decrease on the other side of
x  a (i.e. the limit does not exist).
To determine if the limit is ∞, –∞, or DNE, we need to analyze a few values of x close to
a and on both sides of a as shown in the example(RS2) at right.
Find the following limits.
x2  4 x  5
1. lim 2
x 5
x  25
2. lim
x 7
3. lim
x4
x 1
x  6x  7
2
5
 x  4
2
x2
4. lim
x 1 ( x  1) 2
5. lim
x 0
x3  2
x