1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Algebra of Limits
If f1x=x2+1...
Question
If
f
1
(
x
)
=
x
2
+
10
∀
x
∈
R
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
∀
n
≥
2
,
n
∈
N
, then evaluate
lim
n
→
∞
f
n
(
x
)
Open in App
Solution
f
1
(
x
)
=
x
2
+
10
⟹
f
1
1
(
x
)
=
1
2
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
⟹
f
1
n
(
x
)
=
f
1
1
(
f
n
−
1
(
x
)
)
f
1
n
−
1
(
x
)
=
f
1
n
−
1
(
x
)
2
f
1
n
(
x
)
f
1
n
−
1
(
x
)
=
1
2
f
1
n
(
x
)
f
1
n
−
1
(
x
)
f
1
n
−
1
(
x
)
f
1
n
−
2
(
x
)
⋯
⋯
f
1
2
(
x
)
f
1
1
(
x
)
=
(
1
2
)
n
−
1
⟹
f
1
n
(
x
)
=
2
−
n
⟹
f
n
(
x
)
=
2
−
n
x
+
c
f
1
(
x
)
=
x
2
+
c
=
x
2
+
10
⟹
c
=
10
f
n
(
x
)
=
2
−
n
+
10
lim
x
→
∞
f
n
(
x
)
=
lim
x
→
∞
2
−
n
x
+
10
=
10
Suggest Corrections
0
Similar questions
Q.
If
f
1
(
x
)
=
x
2
+
10
,
∀
x
ϵ
R
, and define
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
,
∀
n
≥
2
, and
lim
n
→
∞
f
n
(
x
)
=
g
(
x
)
, and
∫
g
(
x
)
−
1
1
2
g
(
x
)
(
s
i
n
x
1
+
x
a
)
<
2
g
(
x
)
−
2
, then minimum odd value of a(a > 1) is
Q.
If
f
1
(
x
)
=
x
x
−
1
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
for
n
≥
2
, then the integral value of
x
that satisfies
f
101
(
x
)
=
3
x
is
Q.
If
f
1
(
x
)
=
x
x
−
1
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
for
n
≥
2
, then the integral value of
x
that satisfies
f
101
(
x
)
=
3
x
is
Q.
If
f
1
(
x
)
=
|
|
x
|
−
2
|
and
f
n
)
x
)
=
∣
∣
f
n
−
1
(
x
)
−
2
∣
∣
for all
n
≥
2
,
n
∈
N
, then number of solution of the equation
f
2015
(
x
)
=
2
is
Q.
Let
f
(
x
)
=
3
4
x
+
1
,
and
f
n
(
x
)
be defined as
f
2
(
x
)
=
f
(
f
(
x
)
)
and for
n
≥
2
,
f
n
+
1
(
x
)
=
f
(
f
n
(
x
)
)
.
If
λ
=
lim
n
→
∞
f
n
(
x
)
,
then
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Algebra of Limits
MATHEMATICS
Watch in App
Explore more
Algebra of Limits
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app