[Discuss TrueFalse problems on page 70.]
1. “If
f
is a function, then
f
(
s
+
t
) =
f
(
s
) +
f
(
t
).”
..?.
.
False.
Example:
f
(
x
) =
x
2
,
s
=
t
= 1.
Note however that it IS true that (
f
+
g
)(
t
) =
f
(
t
) +
g
(
t
); that’s
the definition of
f
+
g
.
2. “If
f
(
s
) =
f
(
t
), then
s
=
t
.”
..?.
.
False.
Example:
f
(
x
) =
x
2
,
s
= –1,
t
= 1.
Note however that the converse is true: if
s
=
t
then
f
(
s
) =
f
(
t
).
3. “A vertical line intersects the graph of a function at most
once.”
..?.
.
True.
This is the vertical line test.
4. “If
f
and
g
are functions, then
f
°
g
=
g
°
f
.”
..?.
.
False.
Example:
f
(
x
) =
x
+1,
g
(
x
) =
x
2
.
Or:
f
(
x
) =
x
+1,
g
(
x
) = 2
x
.
Or:
f
(
x
) = 2,
g
(
x
) = 3 for all
x
.
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View Full Document5. “lim
x
→
4
((2
x
)/(
x
–4) – 8/(
x
–4)) = lim
x
→
4
(2
x
)/(
x
–4) – lim
x
→
4
8/(
x
–4).”
..?.
.
False.
The two limits on the right hand side do not exist, so
Limit Law 2 does not apply.
(In fact, the limit on the left
hand side equals 2.)
6. “lim
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 Fall '11
 Staff
 Calculus, Limit, Lefthandedness, right hand, Discuss TrueFalse problems

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