GATE Civil Engineering
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The error in $\dfrac{d}{dx} f(x) \mid_{x=x_0}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\dfrac{d}{dx} f(x) \mid_{x=x_0} \approx \dfrac{f(x_0+h)-f(x_0-h)}{2h}$, is $2 \times 10^{-3}$. The values of $x_0$ and $f(x_0)$ are $119.78$ and $500.01$, respectively. The corresponding error in the central difference estimate for $h=0.02$ is approximately

  1. $1.3 \times 10^{-4}$
  2. $3.0 \times 10^{-4}$
  3. $4.5 \times 10^{-4}$
  4. $9.0 \times 10^{-4}$
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