(a) Write down the Lagrange's polynomial through (xo, fo), (x1, f1), (x2, f2). Hence express 3x2+x+1 (х—1)(ӕ-2)(ӕ-3) as sum of partial fractions. (b) Use Lagrange Interpolation Formula to find a third order polynomial that interpolates all the following values. 0 1 2 4 5 f(x) 3 6 11 30 75 158 291
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![(a) Write down the Lagrange's polynomial through
(xo, fo), (x1, f1), (x2, f2). Hence express
3x2+x+1
(x-1)(x-2)(x-3)
as sum of partial fractions.
(b) Use Lagrange Interpolation Formula to find a third order polynomial that interpolates all
the following values.
0 1
2
3
4
6
f(x) 3
6.
11
30
75
158
291
(c) Show that D = A - + -4+...]
(d) Interpolate the missing entries
1
2
3
4
6.
f(x) 0
10
18
40
а
с
(e) Find the value of ſo" e² dæ taking n = 6, correct to 5 significant figures by Simpson's
one-third rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9975a1be-4a4d-45c3-8d77-81b05a939316%2F70a02c7b-6e25-45ec-865c-c45a42ef8787%2Fcua9wj5_processed.jpeg&w=3840&q=75)
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