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Maximum Error Estimate
If:
$$|f''(x)|\leq M$$
on the interval containing $$a$$ and $$x$$, then the linear approximation error satisfies:
$$|E(x)|\leq\frac{M}{2}|x-a|^2$$
Usage
- Used to obtain an upper bound for the error in linear approximation.
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Maximum Error Estimate
If:
$$|f''(x)|\leq M$$
on the interval containing $$a$$ and $$x$$, then the linear approximation error satisfies:
$$|E(x)|\leq\frac{M}{2}|x-a|^2$$
Usage
- Used to obtain an upper bound for the error in linear approximation.
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