Chapter 2 | Limits
177
113. lim x →6 ⎡ 114. lim x →6 ⎛
⎣ ( x +1) · f ( x ) ⎤ ⎦
⎝ f ( x ) · g ( x )− h ( x ) ⎞ ⎠
[T] In the following exercises, use a calculator to draw the graph of each piecewise-defined function and study the graph to evaluate the given limits.
⎧ ⎩ ⎨ x 2 , x ≤3 x +4, x >3
115. f ( x ) =
f ( x ) f ( x )
lim x →3 − lim x →3 +
a.
b.
⎧ ⎩ ⎨ x 3 −1, x ≤0 1, x >0
116. g ( x ) =
g ( x ) g ( x )
lim x →0 − lim x →0 +
a.
b.
⎧ ⎩ ⎨ x 2 −2 x +1, x <2 3− x , x ≥2
117. h ( x ) =
h ( x ) h ( x )
lim x →2 − lim x →2 +
a.
b.
In the following exercises, use the following graphs and the limit laws to evaluate each limit.
⎛ ⎝ f ( x )+ g ( x ) ⎞ ⎠
lim x →−3 + lim x →−3 −
118.
⎛ ⎝ f ( x )−3 g ( x ) ⎞ ⎠
119.
f ( x ) g ( x ) 3
120. lim x →0
2+ g ( x ) f ( x )
lim x →−5
121.
⎞ ⎠ 2
122. lim x →1 ⎛
⎝ f ( x )
f ( x )− g ( x ) 3
123. lim x →1
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