1
GATE ECE 2015 Set 3
Numerical
+1
-0
The Newton-Raphson method is used to solve the equation $$f\left( x \right) = {x^3} - 5{x^2} + 6x - 8 = 0.$$ Taking the initial guess as $$x=5$$, the solution obtained at the end of the first iteration is ________.
2
GATE ECE 2011
+1
-0.3
A numerical solution of the equation $$f\left( x \right) = x + \sqrt x - 3 = 0$$ can be obtained using Newton $$-$$ Raphson method. If the starting values is $$x=2$$ for the iteration then the value of $$x$$ that is to be used in the next step is
A
$$0.306$$
B
$$0.739$$
C
$$1.694$$
D
$$2.306$$
3
GATE ECE 2010
+1
-0.3
Consider a differential equation $${{dy\left( x \right)} \over {dx}} - y\left( x \right) = x\,\,$$ with initial condition $$y(0)=0.$$ Using Euler's first order method with a step size of $$0.1$$ then the value of $$y$$ $$(0.3)$$ is
A
$$0.01$$
B
$$0.031$$
C
$$0.0631$$
D
$$0.1$$
4
GATE ECE 2008
+1
-0.3
The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is
A
$${x_{n + 1}} = {e^{ - {x_n}}}$$
B
$${x_{n + 1}} = {x_n} - {e^{ - {x_n}}}$$
C
$${x_{n + 1}} = {{\left( {1 + {x_n}} \right){e^{ - {x_n}}}} \over {\left( {1 + {e^{ - {x_n}}}} \right)}}$$
D
$${x_{n + 1}} = {{x_n^2 - {e^{ - {x_n}}}\left( {1 + {x_n}} \right) - 1} \over {{x_n} - {e^{ - {x_n}}}}}$$
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