1
GATE ME 2016 Set 1
Numerical
+2
-0
Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.
2
GATE ME 2016 Set 1
Numerical
+2
-0
Gauss-Seidel method is used to solve the following equations (as per the given order). $${x_1} + 2{x_2} + 3{x_3} = 5$$$$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$\,3{x_1} + 2{x_2} + {x_3} = 3$$\$
Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.
3
GATE ME 2016 Set 2
Numerical
+2
-0
The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,}$$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi$$ is _________.
4
GATE ME 2015 Set 3
Numerical
+2
-0
Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$ If the initial guess is $${x_0} = 1,$$ then the value of $$x$$ after $${2^{nd}}$$ iteration is ___________.