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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) $9.0 \times 10^{-4}$

1 Answer - 5876 Votes

3537

Answer Key : (D) -

$9.0 \times 10^{-4}$



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