Question

1. Divided differences method can be used when the given independent variable value are:
(a) At equal intervals
(b) At unequal intervals
(c) Not well defined
(d) All the above
of the argument.
2. Divided differences are independent of the
(a) Size
(b) Functions
(c) Order
(d) Value
3. In the second derivative using newton's forward difference formula, what is the coefficient of
13f(a).
1
(b)
(a)
h2
(c)
(c) -h2
h2
4. Laplace transform of sinx
(a)
1
(b) 2+1
S​

Answer 1

Answer:

B

A

C

D is the answer

Mark me brainliest

Answer 2

Answer:

1. The Dividend differences method can be used, when the given independent variable values are at unequal intervals. That is option $(b)$.

2. The Divided differences are independent of order. That is, option $(c)$.

3. Using Newton's forward difference formula, in second derivative, the coefficient of 13f is zero.

4. The Laplace transform of $sin(x)$ is $\frac{1}{s^{2} +1}$.

Step-by-step explanation:

• In Newton’s divided difference interpolation method, the independent variables are at unequally intervals. Thus, in this method, the variation in function f(x) and also variation in x is considered.
• .One of the properties of divided differences states that, “The divided differences are symmetrical in all arguments” This implies that, no value of divided difference is affected by order of the argument.
• The second derivative in Newton’s forward difference table  is given by, $(\frac{d^{2}y }{dx^{2} } = \frac{1}{h^{2}}$$($Δ$y -$ Δ$3y+...)$

• The Laplace transform of $sin(kx)$ is $\frac{k}{k^{2} +1}$.

Thus, when k is substituted with 1, Laplace transform of $sinx$ is $\frac{1}{s^{2}+1}$.