Calculus Volume 1

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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