## Marks 1

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The quadratic approximation of $$f\left( x \right) = {x^3} - 3{x^2} - 5\,\,$$ at the point $$x=0$$ is
GATE CE 2016 Set 2
The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point functio...
GATE CE 2012
The Newton-Raphson iteration $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {R \over {{x_n}}}} \right)$$ can be used to comp...
GATE CE 2008
Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are
GATE CE 2007
The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ ...
GATE CE 2007
Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$...
GATE CE 2005
Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}... GATE CE 1995 Given the differential equation$${y^1} = x - y$$with initial condition$$y(0)=0.$$The value of$$y(0.1)$$calculated ... GATE CE 1993 ## Marks 2 More Consider the equation$${{du} \over {dt}} = 3{t^2} + 1$$with$$u=0$$at$$t=0.$$This is numerically solved by using th... GATE CE 2017 Set 1 Newton-Raphson method is to be used to find root of equation$$\,3x - {e^x} + \sin \,x = 0.\,\,$$If the initial trial v... GATE CE 2016 Set 1 For step-size,$$\Delta x = 0.4,$$the value of following integral using Simpson's$$1/3$$rule is ______ GATE CE 2015 Set 2 In Newton-Raphson iterative method, the initial guess value$$\left( {{x_{ini}}} \right)$$is considered as zero while f... GATE CE 2015 Set 2 The quadratic equation$${x^2} - 4x + 4 = 0$$is to be solved numerically, starting with the initial guess$${x_0} = 3.$... GATE CE 2015 Set 1 The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,}$$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as well as n... GATE CE 2015 Set 1 There is no value of $$x$$ that can simultaneously satisfy both the given equations. Therefore, find the 'least squares ... GATE CE 2013 The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{... GATE CE 2011 The table below gives values of a function$$f(x)$$obtained for values of$$x$$at intervals of$$0.25$$The value o... GATE CE 2010 The area under the curve shown between$$x=1$$and$$x=5$$is to be evaluated using the trapezoidal rule. The following ... GATE CE 2009 If the interval of integration is divided into two equal intervals of width$$1.0,$$the value of the definite integral ... GATE CE 2008 Given$$a>0,$$we wish to calculate its reciprocal value$${1 \over a}$$by using Newton - Raphson method for$$f(x)=0.$...
GATE CE 2005

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