Chapter 2 | Limits
155
z −1 z 2 ( z +3)
x 2 −4 x 2 + x −6
41. lim z →0
38. lim x →2
z −1 z 2 ( z +3 )
z −1 z 2 ( z +3 )
x 2 −4 x 2 + x −6
x 2 −4 x 2 + x −6
z
z
x
x
−0.1
a.
0.1
e.
1.9
a.
2.1
e.
−0.01
b.
0.01
f.
1.99
b.
2.01
f.
−0.001
c.
0.001
g.
1.999
c.
2.001
g.
−0.0001 d.
0.0001 h.
1.9999 d.
2.0001 h.
cos t t
(1−2 x )
39. lim x →1
lim t →0 +
42.
1−2 x
1−2 x
x
x
cos
t
t
t
0.9
a.
1.1
e.
0.1
a.
0.99
b.
1.01
f.
0.01
b.
0.999
c.
1.001
g.
0.001
c.
0.9999 d.
1.0001 h.
0.0001 d.
5 1− e 1/ x
40. lim x →0
1− 2 x x 2 −4
43. lim x →2
5 1− e 1/ x
5 1− e 1/ x
x
x
1− 2 x x 2 −4
1− 2 x x 2 −4
x
x
−0.1
a.
0.1
e.
1.9
a.
2.1
e.
−0.01
b.
0.01
f.
1.99
b.
2.01
f.
−0.001
c.
0.001
g.
1.999
c.
2.001
g.
−0.0001 d.
0.0001 h.
1.9999 d.
2.0001 h.
[T] In the following exercises, set up a table of values and round to eight significant digits. Based on the table of values, make a guess about what the limit is. Then, use a
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