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Question 26 - Week 7 Practice | Prasnya
Q26
00:00
3 Dec 2023
Q26.
Given a function
f
(
x
)
=
{
∣
x
∣
x
,
x
≠
0
,
1
,
x
=
0.
f(x)=\begin{cases}\frac{|x|}{x}, & x\ne0,\\ 1, & x=0.\end{cases}
f
(
x
)
=
{
x
∣
x
∣
,
1
,
x
=
0
,
x
=
0.
Which of the following options is/are true?
A
lim
x
→
0
+
f
(
x
)
=
f
(
0
)
\lim_{x\to0^+} f(x)=f(0)
lim
x
→
0
+
f
(
x
)
=
f
(
0
)
.
B
lim
x
→
0
−
f
(
x
)
\lim_{x\to0^-} f(x)
lim
x
→
0
−
f
(
x
)
does not exist.
C
f
f
f
is not continuous at
x
=
0
x=0
x
=
0
.
D
f
f
f
is differentiable at
x
=
0
x=0
x
=
0
.
Save
Check
Details
Q26
00:00
3 Dec 2023
Q26.
Given a function
f
(
x
)
=
{
∣
x
∣
x
,
x
≠
0
,
1
,
x
=
0.
f(x)=\begin{cases}\frac{|x|}{x}, & x\ne0,\\ 1, & x=0.\end{cases}
f
(
x
)
=
{
x
∣
x
∣
,
1
,
x
=
0
,
x
=
0.
Which of the following options is/are true?
A
lim
x
→
0
+
f
(
x
)
=
f
(
0
)
\lim_{x\to0^+} f(x)=f(0)
lim
x
→
0
+
f
(
x
)
=
f
(
0
)
.
B
lim
x
→
0
−
f
(
x
)
\lim_{x\to0^-} f(x)
lim
x
→
0
−
f
(
x
)
does not exist.
C
f
f
f
is not continuous at
x
=
0
x=0
x
=
0
.
D
f
f
f
is differentiable at
x
=
0
x=0
x
=
0
.
Save
Check
Details
