Question 40 - Week 7 Practice | Prasnya
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Week 7
Question 40
00:00
Est. 3 min
Marks:
+5.00
0.00
Consider a function
f
f
defined as
f
(
x
)
=
{
1
e
1
/
x
+
1
,
x
≠
0
0
,
x
=
0.
f(x)=\begin{cases}\frac{1}{e^{1/x}+1},&x\ne0\\0,&x=0.\end{cases}
Which of the following option(s) is/are true?
Multiple correct
MEDIUM Difficulty
20 November 2022
A
f
f
is an unbounded function on
R
\mathbb{R}
.
B
lim
x
→
0
−
f
(
x
)
≠
lim
x
→
0
+
f
(
x
)
\lim_{x\to0^-}f(x)\ne\lim_{x\to0^+}f(x)
.
C
lim
x
→
7
−
f
(
x
)
=
lim
x
→
7
+
f
(
x
)
\lim_{x\to7^-}f(x)=\lim_{x\to7^+}f(x)
.
D
f
f
is continuous at
x
=
0
x=0
.
E
f
f
is continuous at
x
=
7
x=7
.
