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PRECALCULUS Name___________________________________
Limits Practice Date________________ Period____
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Evaluate each limit. Check your work using your graphing calculator.
1) lim (x − 2) 2) lim −s
x→1 s→−2
( )
3) lim 2t 4) lim s + 2
t→1 s→0
( )
5) lim 2 6) lim 2t + 2
w→−3 t→0
( )
7) lim −r − 5 8) lim −2w
r→0 w→2
( ) ( )
9) lim w + 1 10) lim −r + 3
w→−1 r→−2
( 3 2 ) 3
11) lim −w − 5w − 3w + 2 12) lim − 2x + 2
w→−3 x→−1
( 3 2 ) ( 2 )
13) lim −x + 10x − 33x + 38 14) lim −2s + 8s − 8
x→3 s→2
2 ( 2 )
s 11 16) lim −s + 8s − 17
15) lim ( + 3s + ) s→3
s→0 2 2
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( 2 ) 2
17) lim −w + 1 w 1
w→−2 18) lim − + 3w −
w→0 ( 2 2)
( 2 )
19) lim 2x + 3 20) lim 2t + 8t + 8
x→3 t→−2
( )
21) lim 2cot 2w 15
3π 22) lim
w→ t→−1 t2 + 5
4
( ) 2
23) lim −2cos 2r t − 2t − 15
2π 24) lim
r→
3 t→2 t − 5
t + 4 w + 6
25) lim 2 26) lim 2
t→−1 t + 14t + 49 w→−3 w + 8w + 16
x + 3 25r
27) lim 28) lim − 2
x→3 2x2 + 2x + 1 r→−2 r + 25
( )
29) lim cos s w + 4
s→0 30) lim
w→−2 w2 + 11w + 28
Evaluate each limit.
x2 − 3x t − 2
31) lim − 32) lim − 2
x→3 x − 3 t→2 t − 4
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x2 + 4x + 3 s − 1
33) lim 34) lim 2
x→−3 x + 3 s→1 s − 1
w 1
35) lim − 1
w→0 1 1 + r
+ 1 36) lim
−1 + w r→0 r
f(w) h(r)
6 6
4 4
2 2
−8 −6 −4 −2 2 4 6 8 w −8 −6 −4 −2 2 4 6 8 r
−2 −2
−4 −4
−6 −6
−8 −8
w − 2 r − 1
37) lim 38) lim
w→2 w + 2 − 2 r→1 r − 1
g(w) g(r)
12 1
10 0.9
0.8
8
0.7
6 0.6
4 0.5
2 0.4
0.3
−6 −4 −2 2 4 6 8 10 w 0.2
−2 0.1
−4
0.5 1 1.5 2 r
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−2t − 2, t < −1 −3s + 3
( ) ( ) 40) lim
39) lim h t , h t = {
t→−1 −t, t ≥ −1 s→1 −s + 1
h(t) g(s)
8 8
6 6
4 4
2 2
−8 −6 −4 −2 2 4 6 t −6 −4 −2 2 4 6 8 s
−2 −2
−4 −4
−6 −6
−8 −8
x2 + 1, x ≤ −2 −r2 − 6r − 10, r ≤ −2
( ) ( )
41) lim g x , g x = {
x→−2 ( ) ( )
5, x > −2 42) lim g r , g r = r
r→−2 { − 1, r > −2
g(x) 2
12 g(r)
6
10
4
8
2
6
−10 −8 −6 −4 −2 2 4 6 r
4
−2
2
−4
−10 −8 −6 −4 −2 2 4 6 x
−6
−2
−8
−10
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