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Byju's Answer
Standard XII
Mathematics
Inequalities of Integrals
If y=1+x 1 !+...
Question
If y = 1 +
x
1
!
+
x
2
2
!
+
x
3
3
!
+
.
.
.
.
.
.
,
then
d
y
d
x
=
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
.
Open in App
Solution
If y = 1 +
x
1
!
+
x
2
2
!
+
x
3
3
!
+
.
.
.
.
.
.
d
y
d
x
=
d
d
x
1
+
x
1
!
+
x
2
2
!
+
x
3
3
!
+
.
.
.
.
.
.
=
d
d
x
1
+
d
d
x
x
1
!
+
d
d
x
x
2
2
!
+
d
d
x
x
3
3
!
+
.
.
.
.
=
0
+
1
1
!
d
d
x
x
+
1
2
!
d
d
x
x
2
+
1
3
!
d
d
x
x
3
+
.
.
.
.
.
=
0
+
1
1
!
×
1
+
1
2
!
×
2
x
+
1
3
!
×
3
x
2
+
.
.
.
.
.
.
=
1
+
x
1
!
+
1
3
×
2
!
3
x
2
+
1
4
×
3
!
4
x
3
+
.
.
.
.
.
i
.
e
d
y
d
x
=
1
+
x
1
!
+
1
2
!
x
2
+
1
3
!
x
3
+
.
.
.
.
.
.
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0
Similar questions
Q.
If
y
=
1
-
x
1
!
+
x
2
2
!
-
x
3
3
!
+
x
4
4
!
-
x
5
5
!
+
.
.
.
.
,
then
dy
dx
=
________________________
.
Q.
If
y
=
1
+
x
1
!
+
x
2
2
!
+
x
3
3
!
+
…
Find
d
y
d
x
Q.
Mark the correct alternative in each of the following:
If
y
=
1
+
x
1
!
+
x
2
2
!
+
x
3
3
!
+
.
.
.
, then
d
y
d
x
=
(a) y + 1 (b) y − 1 (c) y (d) y
2
Q.
If
y
=
1
-
x
+
x
2
2
!
-
x
3
3
!
+
x
4
4
!
.....to ∞, then write
d
2
y
d
x
2
in terms of y.
Q.
∫
x
3
x
+
1
d
x
is equal to
(
a
)
x
+
x
2
2
+
x
3
3
-
log
1
-
x
+
C
(
b
)
x
+
x
2
2
-
x
3
3
-
log
1
-
x
+
C
(
c
)
x
-
x
2
2
-
x
3
3
-
log
1
+
x
+
C
(
d
)
x
-
x
2
2
+
x
3
3
-
log
1
+
x
+
C
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