Quantitative Methods Answers

The position ) f (x of a particle moving in a line at various times k
x is given in the
following table. Estimate the velocity and acceleration of the particle at x = 2.1 .

x 1.0 1.2 1.4 1.6 1.8 2.0 2.2
f (x) 2.72 3.32 4.06 4.96 6.05 7.39 9.02

Using finite differences, show that the data

x − 3 − 2 −1 0 1 2 3
f (x) 13 7 3 1 1 3 7
represents a second degree polynomial. Obtain this polynomial using interpolation
and find f(5.2) .

The function ) f (x) = ln(1+ x is to be tabulated at equispaced points in the interval
,2[ using linear interpolation. Find the largest s ]3 tep size h that can be used so that
the error 4
5 10−
≤ × in magnitude

Find all the roots of the equation 0 6 11 6
3 2
x + x + x + = by the Graeffe’s root
squaring method using three squaring.

Using synthetic division and perform two iterations of the Birge-Vieta method to find
the smallest positive root of the equation 0 3 3 3 2
4 3 2
x − x + x − x + = . Use the initial
approximation 5.0 x0 = .

Solve the system equations
4 5x − 2y + z =
6 7x + y − 5z =
10 3x + 7y + 4z =
using LU decomposition method.

Find an interval of unit length which contains the smallest negative root in magnitude
of the equation 12 0
3
x + x + = . Taking the midpoint of this interval as initial
approximation and using Newton-Raphson method find the root correct to three
decimal places.

If 7000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. How many years will it take for your balance to reach 10000 dollars?

a sample fo 6 skyline student was selected and data about their anxiety in taking exams and tests for the spring exam 2014 and the data was recorded as shown in the table..
anxiety score test score after exam (%)
10 2
8 3
2 9
1 7
5 6
6 5

Using Regula Falsi method approximates the root of the following equation upto four decimal places.

f(x)=x=e power -x