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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
If fx is co...
Question
If
f
(
x
)
is continuous in
[
0
,
1
]
and
f
(
1
3
)
=
1
then
lim
n
→
∞
f
(
n
√
9
n
2
+
1
)
is
A
1
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B
0
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C
1
3
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D
none of these
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Solution
The correct option is
A
1
lim
n
→
∞
f
(
n
√
9
n
2
+
1
)
=
lim
n
→
∞
f
⎛
⎜ ⎜ ⎜ ⎜
⎝
n
n
√
9
+
1
n
⎞
⎟ ⎟ ⎟ ⎟
⎠
n
→
∞
1
n
→
0
=
f
(
1
3
)
=
1
Suggest Corrections
0
Similar questions
Q.
Consider
f
(
x
)
=
x
2
+
a
x
+
3
and
g
(
x
)
=
x
+
b
and
F
(
x
)
=
lim
n
→
∞
f
(
x
)
+
x
2
n
g
(
x
)
1
+
x
2
n
If
F
(
x
)
is continuous at
x
=
1
, then
Q.
If
f
(
x
)
is continuous in [0, 1] and
f
(
x
)
=
1
for all rational numbers in [0, 1] then
f
(
1
√
2
)
=
1
.
If true enter 1 else enter 0
Q.
If
f
(
x
)
is a polynomial of degree
n
such that
f
(
0
)
=
0
,
f
(
1
)
=
1
2
,
.
.
.
.
,
f
(
n
)
=
n
n
+
1
, then the value of
f
(
n
+
1
)
is
Q.
If
f
x
=
1
-
1
-
x
2
,
then
f
x
is
(a) continuous on [−1, 1] and differentiable on (−1, 1)
(b) continuous on [−1, 1] and differentiable on
-
1
,
0
∪
0
,
1
(c) continuous and differentiable on [−1, 1]
(d) none of these
Q.
If
f
(
x
)
=
lim
n
→
∞
log
(
x
+
2
)
−
x
2
n
sin
x
x
2
n
+
1
, examine the continuity of
f
(
x
)
at
x
=
1
.
Write
1
if continuous and
0
if not.
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