GO Mechanical

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The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\frac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \frac{\text{Exact value – Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ at $x=\pi /6$ radian, choosing $h=0.1$ radian, is

- $<0.1 \%$
- $> 0.1 \% \text{ and } <1 \%$
- $> 1 \% \text{ and } <5 \%$
- $>5 \%$

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