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Vellore Institute of Technology Engineering Entrance Examination
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Mathematics
List of top Mathematics Questions on Limit and Continuity asked in Vellore Institute of Technology Engineering Entrance Examination
If
f
(
x
)
=
ln
(
x
2
+
e
x
2
+
1
)
f(x) = \ln \left( \frac{x^2 + e}{x^2 + 1} \right)
f
(
x
)
=
ln
(
x
2
+
1
x
2
+
e
)
, then the range of
f
(
x
)
f(x)
f
(
x
)
is:
VITEEE - 2024
VITEEE
Mathematics
Limit and Continuity
Evaluate the limit:
L
=
lim
x
→
0
3
5
x
−
7
x
−
5
x
+
1
(
e
x
−
e
−
x
)
ln
(
1
−
3
x
)
L = \lim_{x \to 0} \frac{35^x - 7^x - 5^x + 1}{(e^x - e^{-x}) \ln(1 - 3x)}
L
=
x
→
0
lim
(
e
x
−
e
−
x
)
ln
(
1
−
3
x
)
3
5
x
−
7
x
−
5
x
+
1
VITEEE - 2024
VITEEE
Mathematics
Limit and Continuity
If
z
r
=
cos
r
α
n
2
+
i
sin
r
α
n
2
z_r = \cos \frac{r\alpha}{n^2} + i \sin \frac{r\alpha}{n^2}
z
r
=
cos
n
2
r
α
+
i
sin
n
2
r
α
, where
r
=
1
,
2
,
3
,
.
.
.
,
n
r = 1, 2, 3, ..., n
r
=
1
,
2
,
3
,
...
,
n
, then the value of
lim
n
→
∞
z
1
z
2
z
3
.
.
.
z
n
\lim_{n \to \infty} z_1 z_2 z_3 ... z_n
lim
n
→
∞
z
1
z
2
z
3
...
z
n
is:
VITEEE - 2024
VITEEE
Mathematics
Limit and Continuity