# The error in $\left.\frac{\mathrm{d}}{\mathrm{d} x} f(x)\right|_{x=x_{0}}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\left.\frac{\mathrm{d}}{\mathrm{d} x} f(x)\right|_{x=x_{0}} \approx \frac{f\left(x_{0}+h\right)-f\left(x_{0}-h\right)}{2 h},$ is $2 \times 10^{-3} .$ The values of $x_{0}$ and $f\left(x_{0}\right)$ are 19.78 and 500.01 , respectively. The corresponding error in the central difference estimate for $h=0.02$ is approximately (A) $1.3 \times 10^{-4}$ (B) $3.0 \times 10^{-4}$ (C) $4.5 \times 10^{-4}$ (D) $9.0 \times 10^{-4}$

## Question ID - 155775 | Toppr Answer The error in $\left.\frac{\mathrm{d}}{\mathrm{d} x} f(x)\right|_{x=x_{0}}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\left.\frac{\mathrm{d}}{\mathrm{d} x} f(x)\right|_{x=x_{0}} \approx \frac{f\left(x_{0}+h\right)-f\left(x_{0}-h\right)}{2 h},$ is $2 \times 10^{-3} .$ The values of $x_{0}$ and $f\left(x_{0}\right)$ are 19.78 and 500.01 , respectively. The corresponding error in the central difference estimate for $h=0.02$ is approximately (A) $1.3 \times 10^{-4}$ (B) $3.0 \times 10^{-4}$ (C) $4.5 \times 10^{-4}$ (D) $9.0 \times 10^{-4}$

$9.0 \times 10^{-4}$