Nevilles Method for approximation

emptymaximum
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basically, i don't get it at all.
i understand that

x0 P0
P01
x1 P1 P012
P12
x2 P2

let's approximate f(x) where x is some number.

i have some Pi given and a Pi(i+1) and Pi(i+1)(i+2)
i also have the xi
i don't know what f(x) is, some unknown function.
how do i find the Pi(i+1)(i+2)?

one question i have is to fill the table.
i have another question where I'm supposed to approximate
\sqrt{3} by using f(x) = 3^x and i have values for x0 through x4, so being able to build that table and i'll be able to do that no problem right?

what i have done so far:
nothing, i don't know how to build the table. alls i want help with is table building please.
 
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UPDATE:

i figured out how to make the table by interpolating tables given.
thanks anyways.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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