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Byju's Answer
Standard XII
Chemistry
Characteristics of Equilibrium Constant
The value of ...
Question
The value of a function f(x) are tabulated below
x
0
1
2
3
f(x)
1
2
1
10
Using Newton's forward difference formula, the cubic polynomial that can be fitted to the above data, is
A
2
x
3
+
7
x
2
−
6
x
+
2
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B
2
x
3
−
7
x
2
+
6
x
−
2
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C
x
3
−
7
x
2
−
6
x
+
1
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D
2
x
3
−
7
x
2
+
6
x
+
1
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Solution
The correct option is
D
2
x
3
−
7
x
2
+
6
x
+
1
The difference table is shown as:
By Newton's forward difference formula,
f
(
a
+
n
h
)
=
f
(
a
)
+
n
Δ
f
(
a
)
+
n
(
n
−
1
)
2
!
Δ
2
f
(
a
)
+
n
(
n
−
1
)
(
n
−
2
)
3
!
Δ
3
f
(
a
)
+
.
.
.
⇒
f
(
x
)
=
f
(
0
)
+
x
Δ
f
(
0
)
+
x
(
x
−
1
)
2
!
Δ
2
f
(
0
)
+
x
(
x
−
1
)
(
x
−
2
)
3
!
Δ
3
f
(
0
)
+
.
.
.
.
.
.
.
.
⎡
⎢
⎣
a
+
n
h
=
x
0
+
n
×
1
=
x
n
=
x
⎤
⎥
⎦
=
1
+
x
×
1
+
x
(
x
−
1
)
2
!
×
(
−
2
)
+
x
(
x
−
1
)
(
x
−
2
)
3
!
×
12
=
1
+
x
−
(
x
2
−
x
)
+
2
[
x
(
x
2
−
3
x
+
2
x
)
]
=
1
+
x
−
x
2
+
x
+
2
x
3
−
6
x
2
+
4
x
=
2
x
3
−
7
x
2
+
6
x
+
1
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1
Similar questions
Q.
The values of a function f(x) are tabulaed below
x
0
1
2
3
f(x)
1
2
1
10
Using Newton's forward difference formula, the cubic polynomial that can be fitted to the above data, is
Q.
A function f:
R
→
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satisfies
sin
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f
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y
)
−
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x
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2
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)
]
=
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x
sin
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x
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y
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f
(
2
x
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y
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]
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If
f
′
(
0
)
=
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, then
Q.
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f
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is such that
f
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x
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f
′′
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Q.
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(
x
)
∀
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∫
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f
(
x
)
d
x
=
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2
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x
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Define a sequence
⟨
f
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(
x
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,
f
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,
f
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x
)
,
…
⟩
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,
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)
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−
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f
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