AP Calculus AB Quiz
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LIMITS AND CONTINUITY
Question 1
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Let
N
(
x
)
=
{
x
−
4
∣
x
−
4
∣
,
x
≠
4
0
,
x
=
4
N(x)=\begin{cases}\frac{x-4}{|x-4|},&x\ne4\\0,&x=4\end{cases}
N
(
x
)
=
{
∣
x
−
4∣
x
−
4
,
0
,
x
=
4
x
=
4
. Is
N
N
N
continuous at
x
=
4
x=4
x
=
4
, and why?
A
No;
lim
x
→
4
N
(
x
)
=
0
\lim_{x\to4}N(x)=0
lim
x
→
4
N
(
x
)
=
0
but
N
(
4
)
=
0
N(4)=0
N
(
4
)
=
0
.
B
Yes; both one-sided limits equal
0
0
0
and
N
(
4
)
=
0
N(4)=0
N
(
4
)
=
0
.
C
No;
lim
x
→
4
−
N
(
x
)
=
−
1
\lim_{x\to4^-}N(x)=-1
lim
x
→
4
−
N
(
x
)
=
−
1
and
lim
x
→
4
+
N
(
x
)
=
1
\lim_{x\to4^+}N(x)=1
lim
x
→
4
+
N
(
x
)
=
1
, so the limit does not exist.
D
No;
N
(
4
)
N(4)
N
(
4
)
is undefined.
E
Yes;
N
(
4
)
=
0
N(4)=0
N
(
4
)
=
0
so continuity holds.
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