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)
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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 __________.
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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 ______
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4
GATE CE 2015 Set 1
MCQ (Single Correct Answer)
+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
Fluid Mechanics and Hydraulic Machines
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