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Byju's Answer
Standard XII
Physics
Introduction
If fx=xn, t...
Question
If
f
(
x
)
=
x
n
, then find the value of
f
(
1
)
+
f
1
(
1
)
1
!
+
f
2
(
1
)
2
!
+
.
.
.
.
.
.
+
f
n
(
1
)
n
!
, where
f
r
(
x
)
denotes the
r
t
h
derivative of
f
(
x
)
w
.
r
.
t
.
x
Open in App
Solution
f
(
x
)
=
x
n
f
(
x
)
=
1
f
1
(
x
)
=
n
x
n
−
1
f
1
(
1
)
=
n
f
2
(
x
)
=
n
(
n
−
1
)
x
n
−
2
f
2
(
1
)
=
n
(
n
−
1
)
f
3
(
x
)
=
n
(
n
−
1
)
(
n
−
2
)
x
n
−
3
f
3
(
1
)
=
n
(
n
−
1
)
(
n
−
2
)
f
n
(
x
)
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
.
.
[
n
−
(
n
−
1
)
]
x
n
(
n
−
a
)
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
.
.1
f
n
(
1
)
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
.
.1
f
(
1
)
+
f
′
(
1
)
1
!
+
f
2
(
1
)
2
!
+
.
.
.
.
.
+
f
n
(
1
)
n
!
=
1
+
n
1
!
+
n
1
!
+
n
(
n
−
1
)
2
!
+
.
.
.
.
+
n
(
n
−
1
)
(
n
−
2
)
.
.
.
.1
n
!
=
1
+
n
C
1
+
n
C
2
+
.
.
.
.
+
n
C
n
=
n
C
0
+
n
C
1
+
n
C
2
+
.
.
.
.
.
+
n
C
n
=
2
n
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0
Similar questions
Q.
If
f
(
x
)
=
x
n
, then the value of
f
(
1
)
+
f
1
(
1
)
1
!
+
f
2
(
1
)
2
!
+
.
.
.
.
.
.
f
n
(
1
)
n
!
, where
f
r
(
x
)
denotes the
f
r
(
x
)
derivative of
r
t
h
w.r.t.x
Q.
Assertion :Let
f
(
x
)
=
x
n
&
f
′
(
x
)
=
r
!
n
C
r
x
n
−
r
denotes the
r
t
h
order derivative of
f
(
x
)
then
f
(
1
)
+
f
′
(
1
)
1
!
+
f
′′
(
1
)
2
!
+
.
.
.
.
.
+
f
n
(
1
)
n
!
=
2
n
Reason: The sum of binomial coefficients in the expansion of
(
1
+
x
)
n
is
2
n
Q.
If
f
(
x
)
=
x
n
+
4
, then
f
(
1
)
+
f
′
(
1
)
1
!
+
f
′′
(
1
)
2
!
+
f
′′′
(
1
)
3
!
+
…
+
f
n
(
1
)
n
!
=
Q.
I: lf
f
(
x
)
=
(
1
+
x
)
n
, then the value of
f
(
0
)
+
f
′
(
0
)
+
1
2
!
f
′′
(
0
)
+
⋯
+
1
n
!
f
n
(
0
)
is
2
n
II:
f
(
x
)
=
x
n
+
4
, then the value of
f
(
1
)
+
f
′
(
1
)
+
1
2
!
f
′′
(
1
)
+
⋯
+
1
n
!
f
n
(
1
)
is
2
n
+
4
.
Which of the following is correct?
Q.
If
α
occurs
p
times and
β
occurs
q
times in polynomial equation
f
(
x
)
=
0
of degree
n
(
1
<
p
,
q
<
n
)
, then which of the following is not true?
(
where
f
r
(
x
)
represents
r
t
h
derivative of
f
(
x
)
w.r.t.
x
)
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