GATE EE 2015 Set 1 | Numerical Methods Question 3 | Engineering Mathematics

If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?

$$f\left( a \right).\,f\left( b \right) = 0$$

$$f\left( a \right).f\left( b \right) < 0$$

$$f\left( a \right).f\left( b \right) > 0$$

$$f\left( a \right)/f\left( b \right) \le 0$$

GATE EE 2014 Set 3

Numerical

-0

The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error observed at $${2^{nd}}$$ iteration is ___________.

Your input ____

GATE EE 2013

MCQ (Single Correct Answer)

-0.3

When the Newton-Raphson method is applied to solve the equation $$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$ the solution at the end of the first iteration with the initial value as $${x_0} = 1.2$$ is

$$-0.82$$

$$0.49$$

$$0.705$$

$$1.69$$

GATE EE 2009

MCQ (Single Correct Answer)

-0.3

Let $$\,{x^2} - 117 = 0.\,\,$$ The iterative steps for the solution using Newton -Raphson's method is given by

$${x_{k + 1}} = {1 \over 2}\left( {{x_k} + {{117} \over {{x_k}}}} \right)$$

$${x_{k + 1}} = {x_k} - {{117} \over {{x_k}}}$$

$${x_{k + 1}} = {x_k} - {{{x_k}} \over {117}}$$

$${x_{k + 1}} = {x_k} - {1 \over 2}\left( {{x_k} + {{117} \over {{x_k}}}} \right)$$

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