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Quantitative Methods
The time versus velocity data of a particle is given in the table below. Use Lagrange’s
interpolation formula to find the distance moved by a particle and its acceleration at
the end of 3 seconds.
t :0 ,1 ,2, 5
v: 2, 3 ,12 ,147
interpolation formula to find the distance moved by a particle and its acceleration at
the end of 3 seconds.
t :0 ,1 ,2, 5
v: 2, 3 ,12 ,147
Quantitative Methods
The current in an electric circuit is given by
i=t sin t
where t is the time in seconds. Using the bisection method, estimate the time
required for the current to reach 1 amp (correct up to 2 decimal places)
i=t sin t
where t is the time in seconds. Using the bisection method, estimate the time
required for the current to reach 1 amp (correct up to 2 decimal places)
Quantitative Methods
a)Use Newton's method to approximate the root of the equation xsinx =1 in [0,pi/2].Taking x=1 as the initial guess calculate x1,x2,x3(Work to at least 6 decimal places)
b)Show that the equation x^3-3x^2+2x=1 has no root in the interval [-1,1]
b)Show that the equation x^3-3x^2+2x=1 has no root in the interval [-1,1]
Quantitative Methods
Q: The equation x^3+2x^2-5=0 has a positive real root in the interval (1, 2). Write a fixed point iteration method and show that it converges. Starting with initial approximation x=1.5 find the root of the equation. Perform two iterations.
Quantitative Methods
A book binder has one printing press, one binding machine and manuscripts of seven
different books. The time required for performing printing and binding operations for
different printing and binding operations for different books are shown below:
Book 1 2 3 4 5 6 7
Printing Time 20 90 80 20 120 15 65
(Days)
Binding Time 25 60 75 30 90 35 50
(Days)
Find the optimum sequence of processing of the jobs that minimises the total time required.
Also compute the optimal time required.
different books. The time required for performing printing and binding operations for
different printing and binding operations for different books are shown below:
Book 1 2 3 4 5 6 7
Printing Time 20 90 80 20 120 15 65
(Days)
Binding Time 25 60 75 30 90 35 50
(Days)
Find the optimum sequence of processing of the jobs that minimises the total time required.
Also compute the optimal time required.
Quantitative Methods
1.a-Solve 9x^4-18x^3-31x^2 8x 12=0 by ferrari's method. 2.b-solve the equeation in(a) given that the sum of two of its roots is zero
Quantitative Methods
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
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
Quantitative Methods
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) .
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) .
Quantitative Methods
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
,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
Quantitative Methods
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.
3 2
x + x + x + = by the Graeffe’s root
squaring method using three squaring.
