158
Chapter 2 | Limits
g ( x )
f ( x )
lim x →0 +
lim x →0 − lim x →0 +
66.
71.
f ( x )
72.
g ( x )
67. lim x →0
f ( x )
73. lim x →0 74. lim x →1 75. lim x →2
In the following exercises, use the graph of the function y = h ( x ) shown here to find the values, if possible. Estimate when necessary.
f ( x )
f ( x )
In the following exercises, sketch the graph of a function with the given properties. 76. lim x →2 f ( x ) =1, lim x →4 − f ( x ) =3, lim x →4 + f ( x ) =6, f (4) is not defined. 77. lim x → −∞ f ( x ) =0, lim x →−1 − f ( x ) =−∞, lim x →−1 + f ( x ) =∞, lim x →0 f ( x ) = f (0), f (0) =1, lim x →∞ f ( x ) =−∞
f ( x ) =2, lim x →3 −
f ( x ) =−∞,
lim x
78.
→ −∞
h ( x )
lim x →0 − lim x →0 +
68.
f ( x ) =∞, lim x →∞
f ( x ) =2, f (0) = −1 3
lim x →3 +
h ( x )
69.
f ( x ) =2, lim
f ( x ) =−∞,
lim x
79.
→ −∞
x →−2
f ( x ) =2, f (0) =0
lim x →∞
h ( x )
70. lim x →0
80. lim x → −∞
In the following exercises, use the graph of the function y = f ( x ) shown here to find the values, if possible. Estimate when necessary.
f ( x ) =0, lim
f ( x ) =∞, lim
f ( x ) =−∞,
x →−1 −
x →−1 +
f (0) = −1, lim x →1 −
f ( x ) =−∞, lim x →1 +
f ( x ) =∞, lim x →∞
f ( x ) =0
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