In the following exercises, sketch the graph of a function with the given properties. 80. lim x → − ∞ f ( x ) = 0 , lim x → − 1 − f ( x ) = ∞ , lim x → − 1 + f ( x ) = − ∞ , f ( 0 ) = − 1 , lim x → 1 − f ( x ) = − ∞ , lim x → 1 + f ( x ) = ∞ , lim x → ∞ f ( x ) = 0
In the following exercises, sketch the graph of a function with the given properties. 80. lim x → − ∞ f ( x ) = 0 , lim x → − 1 − f ( x ) = ∞ , lim x → − 1 + f ( x ) = − ∞ , f ( 0 ) = − 1 , lim x → 1 − f ( x ) = − ∞ , lim x → 1 + f ( x ) = ∞ , lim x → ∞ f ( x ) = 0
In the following exercises, sketch the graph of a function with the given properties.
80.
lim
x
→
−
∞
f
(
x
)
=
0
,
lim
x
→
−
1
−
f
(
x
)
=
∞
,
lim
x
→
−
1
+
f
(
x
)
=
−
∞
,
f
(
0
)
=
−
1
,
lim
x
→
1
−
f
(
x
)
=
−
∞
,
lim
x
→
1
+
f
(
x
)
=
∞
,
lim
x
→
∞
f
(
x
)
=
0
In the following exercises, sketch the graph of a function with the given properties.
lim f(x) = 0, lim f(x)= − ∞, lim f(x) = ∞, lim f(x) = f(0), f(0) = 1, lim f(x) = - ∞
x→−∞ x→−1− x→1+ x→0 x = ∞
In the following exercises, consider the graph of the function y=f(x) shown here. Which of the statements about y=f(x) are true and which are false? Explain why a statement is false.
lim f(x) = 5
x→6
For the function f(x) = 2/x, calculate lim h->0 (f(1+h) - f(1)) / h
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