1
GATE CE 2007
+1
-0.3
The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for this purpose is ($$k$$ indicates the iteration level)
A
$${X_{k + 1}} = {{2X_k^3 + 9} \over {3X_k^2 + 4}}$$
B
$${X_{k + 1}} = {{3X_k^3 + 9} \over {2X_k^2 + 9}}$$
C
$${X_{k + 1}} = {X_k} - 3_k^2 + 4$$
D
$${X_{k + 1}} = {{4X_k^2 + 3} \over {9X_k^2 + 2}}$$
2
GATE CE 2007
+1
-0.3
Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are
A
$$2$$ and $$3$$
B
$$2$$ and $$4$$
C
$$3$$ and $$4$$
D
$$-2$$ and $$-3$$
3
GATE CE 2005
+1
-0.3
Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ The Newton - Raphson algorithm for the function will be
A
$${X_{k + 1}} = {1 \over 2}\left( {{X_k} + {a \over {{X_k}}}} \right)$$
B
$${X_{k + 1}} = {X_k} + {a \over 2}X_k^2$$
C
$${X_{k + 1}} = 2{X_k} - aX_k^2$$
D
$${X_{k + 1}} = 2{X_k} - {a \over 2}X_k^2$$
4
GATE CE 1995
Subjective
+1
-0
Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}}$$ iteration, the point $$\,{x_{n + 1}}$$ is computed from $${x_n}$$ as
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
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