Thomas Calculus 13th [Solutions]

98 Chapter 2 Limits and Continuity
73. Here is one possibility. 74. Here is one possibility.
75. Here is one possibility. 76. Here is one possibility.
( )
77. Yes. If lim f x
g( x)
2 then the ratio the polynomials leading coefficients is 2, so lim f ( x)
x
g( x)
2 as well.
x
78. Yes, it can have a horizontal or oblique asymptote.
( )
79. At most 1 horizontal asymptote: If lim f x
L
g( x)
, then the ratio of the polynomials leading coefficients is L,
x
( )
so lim
f x L as well.
x
g( x)
80. lim x 9 x 4
x
lim x 9 x 4
x
x 9 x 4
x 9 x 4
lim 5 lim 0
9 4 1 1
1 1
0
x x x x
5
x
9 4
x x
lim ( x 9) ( x 4)
x x 9 x 4
81.
lim
2
x 25
2
x 1
x
2 2
2 2 x 25 x 1
lim x 25 x 1
x
2 2
x 25 x 1
26
x
2 2 25 1
25 x 1 x 1 1
x
2
x
2
lim 26 lim 0 0
x x
1 1
2 2
( 25) ( 1)
lim x x
2 2
x x 25 x 1
82.
2
lim x 3
x
x
2 x 3 x
lim x 3 x
x
2
x 3 x
lim
x 1
3
x
2
3 x
x
2
x
2
2
3
x
3
x
2
2 2
( 3) ( )
lim x x
2
x x 3 x
lim 0
1 1
1 1
0
x
3
2
lim
x x 3 x
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