The error in ddxf(x)∣∣∣x=x0 for a continuous function estimated with h = 0.03 using the central difference formuladdxf(x)∣∣∣x=x0=f(x0+h)−f(x0−h)2h is 2×10−3. The value 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.

The error in ddxf(x)∣∣∣x=x0 for a continuous function estimated

1.	The error in ddxf(x)∣∣∣x=x0 for a continuous function estimated with h = 0.03 using the central difference formuladdxf(x)∣∣∣x=x0=f(x0+h)−f(x0−h)2h is 2×10−3. The value 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.
Answer» The error in ${\begin{matrix} \frac{d}{d x} f (x) \end{matrix} ∣ ∣ ∣}_{x = x_{0}}$ for a continuous function estimated with h = 0.03 using the central difference formula ${\begin{matrix} \frac{d}{d x} f (x) \end{matrix} ∣ ∣ ∣}_{x = x_{0}} = \frac{f (x_{0} + h) - f (x_{0} - h)}{2 h}$ is $2 \times 10^{- 3}$ . The value 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.