Exams › GATE › Engineering Mathematics

Let x² - 117 = 0. The iterative steps for the solution using Newton-Raphson's method is given by

1. xₖ₊₁ = 1/2 (xₖ + 117/xₖ)
2. xₖ₊₁ = xₖ - 117/xₖ
3. xₖ₊₁ = xₖ - xₖ/117
4. xₖ₊₁ = xₖ - 1/2 (xₖ + 117/xₖ)

Correct answer: xₖ₊₁ = 1/2 (xₖ + 117/xₖ)

Solution

The correct option is derived from the Newton-Raphson method, which involves using the function and its derivative to find roots. In this case, the iterative formula simplifies to the average of the current guess and the ratio of the constant to the current guess, effectively refining the estimate for the square root of 117.

Related GATE Engineering Mathematics questions

• The smallest positive root of the equation x⁵ - 5x⁴ - 10x³ + 50x² + 9x - 45 = 0 lies in the range
• For a flowing fluid, a dimensionless combination of velocity (V), length scale (l), and acceleration due to gravity (g) would be
• The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h. The CORRECT expression for the second derivative is
• In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to
• Let r denote number system radix. The only value(s) of r that satisfy the equation √121_r = 11_r, is/are
• The Newton-Raphson iteration xₙ₊₁ = 1/2 (xₙ + R/xₙ) can be used to compute the

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →