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approximation formula?

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nak:
i got no clue what this is about.. but i see it in checkpoints but i dont understand checkpoints solutions at all. can someone please explain to me how to use it.
f(x+h) = f(x) - hf'(x)

Toothpaste:
Find the approximate value - find f(x+h)
Find the approximate change - find hf'(x)

Example:
Find the approximate value of 16.08^2, when h is small.

Let f(x) = x^2

f'(x) = 2x

let x = 16 and h = 0.08
so that f(x+h) = f(16.08) = 16.08^2

using f(x+h) = f(x) + hf'(x)
Sub in all values [x=16 and h=0.08]

f(16.08) = f(16) + 0.08f'(16)

= 16^2 + 0.08 * 2(16)
= 256 + 2.56
= 258.56

Check by typing 16.08^2 into your calc. It should be about the same.

nak:
can x be any number at all.. like lets say if it was 15 then h would be 1.08?

Timtasticle:
Yes, but obviously you want h to be as small as possible.

Toothpaste:
Euler's rule is used to find the approximate value of f(x+h), when you are given an equation for f(x).

    * Let x represent the known value of x for which y is known.
    * If no value of x is given, let x represent the initial value (or a value that can be substituted into the given equation).
    * If the question says that x has increased or decreased from p to q or whatever, let x=initial value.
    * Basically let x+h represent the unknown.
    * If the x value decreases, h will be negative.
    * If the x value increases, h will be positive.
    * If no equation is given, use logic. Haha. Eg: sqroot(16.02) , you would then say f(x)=sqroot(x) since you can see that it fits.

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