Kuta Software - Infinite Calculus
Name___________________________________
Evaluating Limits
Date________________ Period____
Evaluate each limit.
1) lim f ( x) , f ( x) =
x→2
− x 2 + 2, x ≠ 2
{
−5,
x=2
2) lim −
x → −2
x2 − 4
x+2
f(x)
f(x)
12
4
10
2
8
−6
−4
−2
2
4
6
8
10 x
6
−2
4
−4
2
−6
−10
−8
−6
−4
−2
2
4
6 x
−8
−2
−10
−4
Evaluate each limit. You may use the provided graph to sketch the function.
x 2 − 7 x + 12
3) lim
x→3
x−3
4) lim
x → −3
x+3
x + 2x − 3
2
f(x)
f(x)
8
6
6
4
4
2
2
−4
−2
2
4
6
8
10
x
−10
−2
−8
−6
−4
−2
2
4
x
−2
−4
−4
−6
−6
−8
−8
Evaluate each limit.
5) lim f ( x) , f ( x) =
x→0
{
x + 1, x ≠ 0
2,
x=0
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6) lim f ( x) , f ( x) =
x→3
-1-
{
2+
2,
x
, x≠3
2
x=3
Worksheet by Kuta Software LLC
x2 − 1
7) lim −
x→1
x−1
x2 − 5x
8) lim −
x→5
x−5
x2 − x − 2
9) lim −
x→2
x−2
x 2 + 3 x − 10
10) lim
x → −5
x+5
1
1
+
−4 + x 4
11) lim
x→0
x
13) lim
x→5
x−5
x+4 −3
12) lim
x → −3
14) lim
x→3
x
1
1
−
3+x 3
x+6 −3
x−3
Critical thinking questions:
15) Give an example of a limit of a rational function
where the limit at -1 exists, but the rational
function is undefined at -1.
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16) Give two values of a where the limit cannot be
solved using direct evaluation. Give one value
of a where the limit can be solved using direct
evaluation.
x
lim
→
x a
1
1
+
−2 + x 2
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Evaluating Limits
Date________________ Period____
Evaluate each limit.
1) lim f ( x) , f ( x) =
x→2
− x 2 + 2, x ≠ 2
{
−5,
x=2
2) lim −
x → −2
x2 − 4
x+2
f(x)
f(x)
12
4
10
2
8
−6
−4
−2
2
4
6
8
10 x
6
−2
4
−4
2
−6
−10
−8
−6
−4
−2
2
4
6 x
−8
−2
−10
−4
4
−2
Evaluate each limit. You may use the provided graph to sketch the function.
x 2 − 7 x + 12
3) lim
x→3
x−3
4) lim
x → −3
x+3
x + 2x − 3
2
f(x)
f(x)
8
6
6
4
4
2
2
−4
−2
2
4
6
8
10
x
−10
−2
−8
−6
−4
−2
2
4
x
−2
−4
−4
−6
−6
−8
−8
−1
−
1
4
Evaluate each limit.
5) lim f ( x) , f ( x) =
x→0
{
x + 1, x ≠ 0
2,
x=0
6) lim f ( x) , f ( x) =
x→3
1
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{
2+
2,
x
, x≠3
2
x=3
7
2
-1-
Worksheet by Kuta Software LLC
x2 − 1
7) lim −
x→1
x−1
x2 − 5x
8) lim −
x→5
x−5
−2
−5
x2 − x − 2
9) lim −
x→2
x−2
x 2 + 3 x − 10
10) lim
x → −5
x+5
−3
−7
1
1
+
−4 + x 4
11) lim
x→0
x
−
12) lim
x → −3
x→5
1
1
−
3+x 3
0
1
16
13) lim
x
x−5
x+4 −3
14) lim
x→3
6
x+6 −3
x−3
1
6
Critical thinking questions:
15) Give an example of a limit of a rational function
where the limit at -1 exists, but the rational
function is undefined at -1.
x2 − 1
Many answers. Ex: lim
x → −1 x + 1
16) Give two values of a where the limit cannot be
solved using direct evaluation. Give one value
of a where the limit can be solved using direct
evaluation.
x
lim
→
x a
1
1
+
−2 + x 2
No direct eval: a=0,2 Direct eval: a=any other number
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-2-
Worksheet by Kuta Software LLC