Answer to Question #60690 in Math for esita

Question

6. a) Find the interpolating polynomial that fits the following data:

(3)

b) Using the Lagrange’s form of an interpolating polynomial find the value of x when y = 3
from the following table of values:

(3)

c) Using Lagrange’s interpolation formula, prove that ) y y y(3.0 y ) y(2.0 y 1 = 3 − 5 − −3 + −3 − −5

approximately. (4)
7. a) Given log 654 .2 8156, log 658 .2 8182, log 659 .2 8189, log 661 .2 8202 10 = 10 = 10 = 10 = , find
656 log10 . (3)
b) Prove that the third divided differences with arguments d ,a of the function ,b ,c
x
1
is equal
to
abcd
1
− . (3)
c) Determine the spacing h in a table of equally spaced values of the function 3
)x(f = x
between 0 and 1, so that quadratic interpolation in this table yields accuracy of 6
1 10−
× . (4)
8. a) Find the value of )5( f′ from the following table
(3)
x 0 0.5 1 1.5 2
f(x) 1.0 1.75 3 4.75 7
x 4 7 10 12
y –1 1 2 4