Quantitative Methods Answers

5.The technique of determining an approximate value of f(x) for a non-tabular value of x which lies in the internal [a, b] is referred to as
a.interpolation
b.extrapolation
c.exterpolation
d.intrapolation

6.If all the elements above the main diagonal of a square matrix vanish, the matrix is known as
a.side triangular
b.half triangular
c.lower triangular
d.upper triangular

3.The zeroeth divided difference of the function f, with respect to \\( x_{i} \\) denoted by \\( f[x_{i}]\\) can be written as
a.\\(f[x] = f(xi)\\)
b.\\(f[x_{0}] = f(x_{i})\\)
c.\\(f[x] = f(x_{i})\\)
d.\\( f[x_{i}] = f(x_{i})\\)

4.When the number of rows is equal to the number of columns in a matrix, it is called _________ matrix
a.square
b.equal
c.similar
d.singular

1.The interpolating polynomial of degree \\(\\leq n\\)with the nodes\\(x_{0}, x_{1},\\cdots, x_{n}\\) can be written as
a.\\( f[x_{i}] = f(x_{i})\\)
b.\\( f[x_{i}] + f(x^i)=1\\)
c.\\( f[x_{i}] - f(x_{i}=0)\\)
d.\\( f[x_{i}] +f(x_{i}=0)\\)

2. A matrix in which all the non-diagonal elements vanish is called ___________ matrix.
a.diagonal
b.vanishing
c.non-diagonal
d.non-vanishing

When you multiply an n digit number by an m digit number manually, then number of digit-wise multiplications you perform is:

scientist why the population of Mathsland continues to grow.]
Year: 1930 1940 1950 1960 1970
Populations: In millions 1.0 1.2 1.6 2.8 5.4
Using a Gregory-Newton method, find the population of the country in 1920?
b) In what year does the expected population reach 60.4 million people?

The equation e^(-Lx)=Lx has a root/zero between x=0 and x=1. This root is approximately at the midpoint of these two x-values. Find this root using a suitable algebra method.
L is 1.55

Evaluate following double integral value taking 4 segment for both x and y direction use Simpson rule ∫(2)_(4)∫(x)_(3x^2) ((3x^2)+y) dy dx

obtain second order derivative y'' using Taylor series Expansion using 4 point

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:
o Gas volume: V = 0.8 m3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done =
i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:
o integral calculus
o Simpson’s rule