AP Calculus BC Quiz
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LIMITS AND CONTINUITY
Question 1
of 20
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For
p
(
x
)
=
{
sin
x
/
x
,
x
≠
0
1
,
x
=
0
p(x)=\begin{cases}\sin x/x,&x\ne0\\1,&x=0\end{cases}
p
(
x
)
=
{
sin
x
/
x
,
1
,
x
=
0
x
=
0
, is
p
p
p
continuous at
x
=
0
x=0
x
=
0
, and why?
A
No;
p
(
0
)
p(0)
p
(
0
)
is undefined, so continuity fails.
B
No;
lim
x
→
0
p
(
x
)
\lim_{x\to0}p(x)
lim
x
→
0
p
(
x
)
does not exist, so continuity fails.
C
Yes;
lim
x
→
0
p
(
x
)
\lim_{x\to0}p(x)
lim
x
→
0
p
(
x
)
exists, so
p
p
p
is continuous at
0
0
0
.
D
Yes;
p
(
0
)
p(0)
p
(
0
)
exists,
lim
x
→
0
p
(
x
)
\lim_{x\to0}p(x)
lim
x
→
0
p
(
x
)
exists, and
lim
x
→
0
p
(
x
)
=
p
(
0
)
\lim_{x\to0}p(x)=p(0)
lim
x
→
0
p
(
x
)
=
p
(
0
)
.
E
No;
lim
x
→
0
p
(
x
)
≠
p
(
0
)
\lim_{x\to0}p(x)\ne p(0)
lim
x
→
0
p
(
x
)
=
p
(
0
)
, so continuity fails.
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