Question 32 - Week 7 Practice | Prasnya
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Week 7
Question 32
00:00
Est. 4 min
Marks:
+5.00
0.00
Define a function
f
(
x
)
=
{
x
−
3
∣
x
−
3
∣
,
x
≠
3
,
1
,
x
=
3.
f(x)=\begin{cases}\frac{x-3}{|x-3|}, & x\ne3,\\ 1, & x=3.\end{cases}
Which of the following options is/are true?
Multiple correct
Medium Difficulty
06 August 2023
A
lim
x
→
3
+
f
(
x
)
=
f
(
3
)
\lim_{x\to3^+}f(x)=f(3)
.
B
lim
x
→
3
−
f
(
x
)
\lim_{x\to3^-}f(x)
does not exist.
C
f
f
is not continuous at
x
=
3
x=3
.
D
f
f
is differentiable at
x
=
3
x=3
.
E
f
′
(
3
)
=
1
f'(3)=1
.
