Confirming Continuity over an Interval
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find
lim
x
→
0
sin
(
x
)
x
\lim_{x \to 0} \frac{\sin(x)}{x}
lim
x
→
0
x
s
i
n
(
x
)
QUESTION
Find the limit:
lim
x
→
3
(
2
x
+
1
)
\lim_{x \to 3} (2x + 1)
lim
x
→
3
(
2
x
+
1
)
.
QUESTION
Find
lim
x
→
2
(
x
2
−
4
)
/
(
x
−
2
)
\text{lim}_{x \to 2} (x^2 - 4)/(x - 2)
lim
x
→
2
(
x
2
−
4
)
/
(
x
−
2
)
. Is it continuous at
x
=
2
x = 2
x
=
2
?
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ANSWER
Limit is
4
4
4
, not continuous without
f
(
2
)
f(2)
f
(
2
)
defined. Use L'Hôpital's rule or factor: limit is
4
4
4
, but function undefined.
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