approximation formula?

[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.

[Daniel15]

That Euler guy has too many things named after him

[Ahmad]

Euler is my favourite mathematician. After he became blind he published I think, over 70 volumes.

He had stunning memory. He memorised the Aeneid of Virgil perfectly, and could even state the first and last line of each page.

He calculated as men breathe. One night he couldn't sleep so calculated the 6th root of numbers upto 200, and surprisingly remembered them all when he woke up.

^^

[bilgia]

errrr.....thats awesome!

[kido_1]

WOW.
That is pretty crazy stuff.