Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For the function
f
(
x
)
=
{
e
1
/
x
−
1
e
1
/
x
+
1
,
x
≠
0
0
,
x
=
0
f(x) = \begin{cases} \frac{e^{1/x} - 1}{e^{1/x} + 1}, & x \neq 0 \\ 0, & x = 0 \end{cases}
f
(
x
)
=
{
e
1/
x
+
1
e
1/
x
−
1
,
0
,
x
=
0
x
=
0
, which of the following is correct (a)
lim
x
→
0
f
(
x
)
\lim_{x \rightarrow 0} f(x)
lim
x
→
0
f
(
x
)
does not exist (b)
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
0
x = 0
x
=
0
(c)
lim
x
→
0
f
(
x
)
=
1
\lim_{x \rightarrow 0} f(x) = 1
lim
x
→
0
f
(
x
)
=
1
(d)
lim
x
→
0
f
(
x
)
\lim_{x \rightarrow 0} f(x)
lim
x
→
0
f
(
x
)
exists but
f
(
x
)
f(x)
f
(
x
)
is not continuous at
x
=
0
x = 0
x
=
0
Browse the problem library