Question

The error in ${\begin{array}{c}\frac{d}{dx}f\left(x\right)\end{array}|}_{x=x_0}$ for a continuous function estimated with h = 0.03 using the central difference formula

${\begin{array}{c}\frac{d}{dx}f\left(x\right)\end{array}|}_{x=x_0}=\frac{f(x_0+h)-f(x_0-h)}{2h}$ is $2\times {10}^{-3}$. The value 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. $9.0\times {10}^{-4}$

Answer 1

The correct option is D $9.0\times {10}^{-4}$


$\frac{e}{2\times {10}^{-3}}={\left(\frac{0.02}{0.03}\right)}^2$
$e=\frac{4\times 2\times {10}^{-3}}{9}$
$=\frac{80}{9}\times {10}^{-4}$
$=9.0\times {10}^{-4}$