The error in \frac{d}{dx}f(x)|._{x = x_{0}} for a continuous function estimated with h = 0.03 using the central difference formula \frac{d}{dx}f(x)|._{x = x_{0}} \approx {f(x_{0} + h)−f(x_{0}−h)}/{2h},\:\text{is}\:2 \times 10^{−3} The values of x 0 and f(x 0 ) are 19.78 and 500.01, respectively. The corresponding error in the central difference estimate for h = 0.02 is approximately

Correct Answer is : 9.0 × 10-4

GATE Civil Engineering (CE) 2012 Solved Paper

Question : 36 of 65

Marks: +1, -0

The error in

\;{d}/{dx}f(x)|._{x = x_{0}}

for a continuous function estimated with h = 0.03 using the central difference formula

\;{d}/{dx}f(x)|._{x = x_{0}} ≈ \;{f(x_{0}\;+\;h)−f(x_{0}−h)}/{2h},\:\;\text "is"\;\:2 × 10^{−3}

The values of x₀ and f(x₀) are 19.78 and 500.01, respectively. The corresponding error in the central difference estimate for h = 0.02 is approximately

1.3 × 10^-4
3.0 × 10-4
4.5 × 10-4
9.0 × 10-4

Validate

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