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c) Solve the IVP
y 1 y , )0(y 0
2
′ = + =
using classical R-K method of h(0 )
4
. Find )4.0(y taking h = 2.0 . Compare the solution
obtained with the exact solution and find the error.
y 1 y , )0(y 0
2
′ = + =
using classical R-K method of h(0 )
4
. Find )4.0(y taking h = 2.0 . Compare the solution
obtained with the exact solution and find the error.
b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )
0. a) Find the solution of the difference equation yk+2 − 4yk+1 + 4yk = ;0 k = ,1,0 K. Also find
the particular solution when 1 y0 = and 6 y1 = .
the particular solution when 1 y0 = and 6 y1 = .
4. a) The Gauss elimination method is used to solve the system of equations
6 x 4x x 1 + 2 + α 3 =
3 2x x 2 x 1 − 2 + α 3 =
5 x 3x x α 1 + 2 + 3 =
Find the value of α for which the system has (i) a unique solution (ii) no solution (iii)
infinitely many solutions
6 x 4x x 1 + 2 + α 3 =
3 2x x 2 x 1 − 2 + α 3 =
5 x 3x x α 1 + 2 + 3 =
Find the value of α for which the system has (i) a unique solution (ii) no solution (iii)
infinitely many solutions
c) Obtain the cube root of 12 using Newton-Raphson formula.
Math
b) Find a root of the equation 0 3x 10x 10x 7
3 2
+ + + = which is close to − 0.2 using the
Birge-Vieta method. Perform two iterations of the method
3 2
+ + + = which is close to − 0.2 using the
Birge-Vieta method. Perform two iterations of the method
Math
1. a) A negative root of smallest magnitude of the equation x 5x 20 0
3
+ + = is to be determined
i) Find an interval of unit length which contains this root
ii) Perform two iterations of the bisection method
iii) Taking the end points of the last interval as initial approximations perform one iteration
of the secant method.
3
+ + = is to be determined
i) Find an interval of unit length which contains this root
ii) Perform two iterations of the bisection method
iii) Taking the end points of the last interval as initial approximations perform one iteration
of the secant method.
The Taylor series about 0 for the function f(x)=sin(x) is x^2-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880.... and the Taylor series about 0 for the function g(x)=e^x is 1+x+(x^2)/2+(x^3)/6+(x^4)/24+(x^5)/120+....What is the coefficient of x^3 in the series for e^x sin(x)?
A third plane can be found that passes through the line of intersection of two existing planes.?
a. Two planes are given by the equations 2x − 3y + z − 6 = 0 and -3x + 5y + 4z + 6 = 0. Find the scalar equation of the plane that passes through the line of intersection of these two planes, and also passes through the point (1, 3, -1).
b. Give the equations of two planes. Create a third plane that passes through the line of intersection of the original two and which is parallel to the z-axis. Explain your reasoning
a. Two planes are given by the equations 2x − 3y + z − 6 = 0 and -3x + 5y + 4z + 6 = 0. Find the scalar equation of the plane that passes through the line of intersection of these two planes, and also passes through the point (1, 3, -1).
b. Give the equations of two planes. Create a third plane that passes through the line of intersection of the original two and which is parallel to the z-axis. Explain your reasoning
Triangle ABC has vertices A(-1, 1, 3), B(-1, 3, 5), and C(-3, 3, 3). What kind of triangle is ΔABC? Justify your answer
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#339914 on Dec 2023
#339914 on Dec 2023