questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Indefinite Integrals
Question 188
Question 188 of 416
Medium
MCQ
If
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
is given by
f
(
x
)
=
x
+
1
f(x)=x+1
f
(
x
)
=
x
+
1
, then the value of
lim
n
→
∞
1
n
[
f
(
0
)
+
f
(
5
n
)
+
f
(
10
n
)
+
⋯
+
f
(
5
(
n
−
1
)
n
)
]
\displaystyle\lim_{n\to\infty}\frac{1}{n}\left[f(0)+f\left(\frac5n\right)+f\left(\frac{10}n\right)+\cdots+f\left(\frac{5(n-1)}{n}\right)\right]
n
→
∞
lim
n
1
[
f
(
0
)
+
f
(
n
5
)
+
f
(
n
10
)
+
⋯
+
f
(
n
5
(
n
−
1
)
)
]
is:
A
3
2
\dfrac32
2
3
B
5
2
\dfrac52
2
5
C
1
2
\dfrac12
2
1
D
7
2
\dfrac72
2
7
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
\[I=\lim_{n\to\infty}\sum_{r=0}^{n-1}f\left(\frac{5r}n\right)\frac1n=\int_0^1f(5x)\,dx=\int_0^1(5x+1)\,dx=\left[\frac{5x^2}2+x\right]_0^1=\frac52+1=\frac72\]
Answer the question to unlock
Previous
Next