Approximation

**Amer** · June 26th 2009, 01:17 AM

I have a question in numerical analysis and I do not know where to put it so I post it here ok the question

Find the largest interval in which $p^{*}$ must lie to approximate $p$ with relative error at most $10^{-4}$ for each value of p

$a.\pi \quad\quad b.e \quad\quad c.\sqrt{2} \quad\quad d.\sqrt[3]{7}$

I know that relative error = $\frac{\mid p-p^*\mid}{\mid p\mid}$

$p^*$ is the approximation to for $p$

can anyone tell me how I can solve questions like this ..........

Thanks

**BobP** · June 26th 2009, 06:53 AM

|p - p*| / |p| <= 10^(-4), so |p - p*| <= |p|.10^(-4).
(a) p = pi.
|pi - p*| <= pi.*10^(-4) = 3.14159 * 0.0001 = 0.000314
so pi - 0.000314 <= p* <= pi + 0.000314

**Amer** · June 26th 2009, 07:02 AM

Originally Posted by BobP

|p - p*| / |p| <= 10^(-4), so |p - p*| <= |p|.10^(-4).
(a) p = pi.
|pi - p*| <= pi.*10^(-4) = 3.14159 * 0.0001 = 0.000314
so pi - 0.000314 <= p* <= pi + 0.000314

can you explain more

you sub pi instead of p

$\mid \pi - p^* \mid \leq \pi(10^{-4})=3.14159(\frac{1}{10000})$

I can't understand what you did in the red line

**BobP** · June 26th 2009, 08:17 AM

The previous line is saying that the maximum difference between the exact and approximate values is to be about 0.000314. In that case the approximate value has to lie within the approximate range 3.141278 to 3.141907.

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