Guide
1
To find the change of any quantity calculate or measure its initial value (x1).
2
calculate or measure the final value of the same magnitude (x2).
3
Find change this value using the formula: Δx = x2-x1.For example, the initial value of the mains voltage U1 = 220 V, the final value - U2 = 120V.The voltage change (or delta voltage) is equal to ΔU = U2-U1 = 220V-120V = 100V
4
To find the absolute error of measurement, determine the exact or as it is sometimes called, the true value of a quantity (x0).
5
Take approximate (measured - measured) value of the same magnitude (x).
6
find the absolute measurement error according to the formula: Δx =
| x-x0 |.For example: the exact number of residents - residents of 8253 (x0 = 8253), and rounding that number to 8300 (the approximate value of x = 8300).The absolute error (or delta X) will be equal to Δx = | 8300-8253 | = 47, and rounding up to 8200 (x = 8200), the absolute error - Δx = | 8200-8253 | = 53.Thus, rounding up to the number 8300 would be more accurate.
7
To compare the values of F (x) in a strictly fixed point x0 with the values of the same function at any other point x in the neighborhood of x0, the notion of "the increment function» (ΔF) and "incrementargument of the function »(Δx).Sometimes Δx called "increment of the independent variable."Find the increment of the argument by the formula Δx = x-x0.
8
Determine the value of the function at the point x0 and x and mark their respective F (x0) and F (x).
9
Calculate the increment of the function: ΔF = F (x) - F (x0).For example: it is necessary to find the increment of the argument and the increment function F (x) = x2 + 1, with the argument changes from 2 to 3. In this case, x0 = 2 and x = 3.
increment argument (or delta X) be Δx = 3-2 = 1.
F (x0) = X02 + 1 = 22 + 1 = 5.
F (x) = x2 + 1 = 32 + 1 = 10.
Increment function (or delta ef) ΔF = F (x) - F (x0) = 10-5 = 5
increment argument (or delta X) be Δx = 3-2 = 1.
F (x0) = X02 + 1 = 22 + 1 = 5.
F (x) = x2 + 1 = 32 + 1 = 10.
Increment function (or delta ef) ΔF = F (x) - F (x0) = 10-5 = 5
Note
not need to subtract a larger number of smaller, but from the endvalue (it does not matter: it is greater or less) starting!
Helpful Hint
If you find all the Δ value is only used in the same units of measurement.
Sources:
- Handbook of mathematics for secondary schools, AGZipkin 1983