What is Newton raphson method method?
Newton's raphson method, also known as the Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots of a real-valued function.
Newton raphson method is one of the fastest convergence method. It is faster than bisection method. It is a linear method of convergence.
Multiple choice questions
1. Rate of convergence of the Newton-Raphson method is generally __________
a) Linear
b) Quadratic
c) Super-linear
d) Cubic
2.Newton-Raphson method is used to find the root of the equation x^2 - 2 = 0. If iterations are started from - 1, then iterations will be
A.converge to -1
B.converge to √2
C.converge to -√2
D.no coverage
3.The Newton-Raphson method of finding roots of nonlinear equations falls under the category of which of the following methods?
a) bracketing
b) open
c) random
d) graphical
4.Using Newton-Raphson method, find a root correct to three decimal places of the question x^3-3x-5=0 .
a.2.275
b.2.279
c.2.222
d.None of these
5. The Iterative formula for Newton Raphson method is given by __________
a) x1 = x0-f(x0)/f’(x0)
b) x0 = x1-f(x0)/f‘(x0)
c) x0 = x1+f(x0)/f’(x0)
d) x1 = x0+f(x0)/f‘(x0)
6. We wish to solve x^2 - 2 = 0 by Newton Raphson technique. If initial guess is x0 = 1.0, subsequent estimate of x (i.e. x1) will be
A.1.414
B.1.5
C.2.0
D.None of these
7.In Newton Raphson method if the curve f f(x) is constant then __________
a) f’(x)=0
b) f(x)=0
c) f’'(x)=0
d) f’(x)=c
8. Double (Repeated) root of 4x^3- 8x^2- 3x + 9 = 0 by Newton-raphson method is
A. 1.4
B. 1.5
C. 1.6
D. 1.55
9. For what values of 0 the initial guess will be equal to the next iterative values?
a) 70 degrees
b) 90 degrees
c) 100 degrees
d) 55 degrees
10.At which point the iterations in the Newton Raphson method are stopped?
a) When the consecutive iterative values of x are not equal
b) When the consecutive iterative values of x differ by 2 decimal places
c) When the consecutive iterative values of x differ by 3 decimal places
d) When the consecutive iterative values of x are equal
11.Using Newton-Raphson method, find a root correct to three decimal places of the equation sin x = 1 - x.
A. 0.511
B. 0.500
C. 0.555
D. None of these
12.The Newton Raphson method fails if __________
a) f’(x0)=0
b) f’’(x0)=0
c) f(x0)=0
d) f’’’(x0)=0
13.In which of the following methods proper choice of initial value is very important?
A. Bisection method
B. False position
C. Newton-Raphson
D. Bairsto method
14.The value of y’/x’ in terms of the angle 0 is given by _____________
a) tanθ
b) secθ
c) cotθ
d) cosecθ
15.The Newton Raphson method is also called as ____________?
a) Tangent method
b) Secant method
c) Chord method
d) Diameter method
16. The equation f(x) is given as x²-4=0. Considering the initial approximation at x=6 then the value of x1 is given as __________
a) 10/3
b) 4/3
c) 7/3
d) 13/3
17.For decreasing the number of iterations in Newton Raphson method.
a) The value of f’(x) must be increased
b) The value of f’’(x) must be decreased
c) The value of f’(x) must be decreased
d) The value of f’’(x) must be increased
18.In Newton Raphson method f’(x) for a given point is given by the formula ____________
a) y/x’
b) y’/x
c) y/x
d) y’/x’
19.If f(x) = x2-117 = 0 then the iterative formula for Newton Raphson Method is given by ____________
a) x(n+1)=0.25 [x(n)+166x(n)]
b) x(n+1)=0.5 [x(n)+166x(n)]
c) x(n+1)=0.5 [x(n)-166x(n)]
d) x(n+1)=0.25 [x(n)-166x(n)]
20.The points where the Newton Raphson method fails are called?
a) floating
b) continuous
c) non-stationary
d) stationary
0 Comments