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TS EAMCET 20-July-2022 Shift 1 Solved Paper
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Section:
Mathematics
© examsiri.com
Question :
76 of 160
Marks:
+1
,
-0
Given that
lim
n
→
∞
1
n
n
p
∑
r
=
1
f
(
r
n
)
=
∫
0
p
f
(
x
)
d
x
. If
f
:
ℝ
→
ℝ
is defined by
f
(
x
)
=
x
2
+
2
, then
lim
n
→
∞
3
n
[
f
(
7
n
)
+
f
(
14
n
)
+
f
(
21
n
)
+
.
.
.
+
f
(
7
)
]
=
55
57
104
7
Validate
Solution:
Given,
lim
n
→
∞
1
n
n
p
∑
r
=
1
f
(
r
n
)
=
p
∫
0
f
(
x
)
dx
f
:
R
→
R
,
f
(
x
)
=
x
2
+
2
Now,
lim
n
→
∞
3
n
[
f
(
7
n
)
+
f
(
14
n
)
+
f
(
21
n
)
+
.
.
.
+
f
(
7
)
]
=
lim
n
→
∞
3
n
[
(
7
n
)
2
+
2
+
(
14
n
)
2
+
2
+
(
21
n
)
2
+
2
+
.
.
.
+
(
7
n
n
)
2
+
2
]
=
lim
n
→
∞
3
n
[
2
n
+
(
7
n
n
)
2
+
(
1
2
+
2
2
+
3
2
+
.
.
.
+
n
2
]
.
=
lim
n
→
∞
3
n
[
2
n
+
49
n
2
n
(
n
+
1
)
(
2
n
+
1
)
6
]
=
lim
n
→
∞
3
[
2
+
49
6
n
2
(
1
+
1
n
)
(
2
+
1
n
)
n
2
]
=
3
[
2
+
49
6
×
2
]
=
55
© examsiri.com
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