Approximating the value of a function

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SUMMARY

The discussion centers on using binary search to approximate the square root of 5 through the function f(x) = x^2 - 5 within the domain [2, 3]. The user successfully calculated values at f(2), f(3), f(2.5), f(2.25), f(2.125), and concluded that f(2.1875) provides an accurate approximation. The accuracy of 1/16 is confirmed by noting that the maximum deviation from 2.1875 is 0.0625, which equals 1/16.

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Yankel
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Hello,

I have a problem which I did solve, but I ain't sure of something in it, something small to be honest.

The question is:

Use a binary search and the function f(x)=x^2-5 in the domain [2,3] to find approximation for the value of the square root of 5, with an accuracy of 1/16.

What I did, I tried finding where the function is equal to 0, i.e. x^2-5=0 meaning x is the square root of 5.

I calculated f(2) and f(3), and then f(2.5), f(2.25), f(2.125) and finally f(2.1875), which is the answer (2.1875 is the answer). My simple question is, how, or where, do I see that I am 1/16 accurate ?

Thank you !
 
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Hi Yankel,

You didn't mention the values for f, but either way, the actual root is either between 2.125 and 2.1875, or between 2.1875 and 2.125.
So the maximum deviation from 2.1875 is 0.0625, which is 1/16.
 

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