1
GATE CE 2016 Set 1
Numerical
+2
-0
Newton-Raphson method is to be used to find root of equation $$\,3x - {e^x} + \sin \,x = 0.\,\,$$ If the initial trial value for the root is taken as $$0.333,$$ the next approximation for the root would be _________ (note: answer up to three decimal)
2
GATE CE 2015 Set 2
Numerical
+2
-0
In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while finding the roots of the equation: $$\,f\left( x \right) = - 2 + 6x - 4{x^2} + 0.5{x^3}.\,\,\,$$ The correction, $$\Delta x,$$ to be added to $${{x_{ini}}}$$ in the first iteration is __________.
3
GATE CE 2015 Set 2
Numerical
+2
-0
For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______
4
GATE CE 2015 Set 1
+2
-0.6
The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,}$$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $${\rm I}$$ is the exact value of the integral obtained analytically and $$J$$ is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?
A
$$J > {\rm I}$$
B
$$J < {\rm I}$$
C
$$J = {\rm I}$$
D
Insufficient data to determine the relationship
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
Joint Entrance Examination