GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/42

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Question 42 (Textile Technology & Fibre Science)

Starting from the initial point $x_0 =10$ , if the sequence { $x_n$ } is generated using Newton Raphson method to compute the root of the equation $x^4-600=0$ , then $x_2$ , accurate to two decimal places, is equal to __5.95 to 6.25__.

Answer / Solution

$f(x)=x^4-600=0$
${f}'(x)=4x^3$
By formula-
By newton Raphsons method-
$x_(n+1)=x_n-\frac{f(x_n)}{{f}'(x_n)}$
$x_1=x_0-\frac{f(x_0)}{{f}'(x_0)}$
Given, $x_0=10$
$x_1=10-\frac{(10)^4-600}{4(10)^3}$
$x_1=7.65$
and
$x_2=x_1-\frac{f(x_1)}{{f}'(x_1)}$
$x_2=7.65-\frac{(7.65)^4-600}{4(7.65)^3}$
$x_2=6.07$ (Ans)

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