indet1:  script to determine an approximation of F(x) knowing an approximation of x.  At the beginning  F(x) = x·sin(x³) is calculated.

function F(x) { with(Math) {
y = x*sin(pow(x,3)
return y
}}

If x = 2 ± 0.05, what is the value of F(x)?  With "click1" I have a quick evaluation. With "click2" I have a better evaluation.

F(x) = 1.74 ± 0.26.

indet2:  script to determine an approximation of F(x,y) knowing approximations of x and y.  At the beginning  F(x,y) = log(x+y)·√(x-y) is calculated.

function F(x,y) { with(Math) {
u = log(x+y)*sqrt(x-y)
return u
}}

If x = 5 ± 0.5, y = 3 ± 0.5, what is the value of F(x,y)?

F(x,y) = 2.84 ± 0.76.

indet3:  script to determine an approximation of F(x,y,z) knowing approximations of x, y and z.  At the beginning  F(x,y,z) = x·y·sin(z·π/180) is calculated.

function F(x,y,z) { with(Math) {
u = x*y*sin(z*PI/180)
return u
}}

If x = 9.80 ± 0.02, y = 0.3 ± 0.006, z = 30 ± 1, what is the value of F(x,y,z)?

 

F(x,y,z) = 1.471 ± 0.077, or 1.47 ± 0.08  (? is about half of 0.3 kg, as we would have expected, taking into account the width of the angle).

indet4:  script to determine an approximation of F(x,y,z,w) knowing approximations of x, y, z, w.  At the beginning  F(x,y,z,w) = (x-y)/(z+w) is calculated.

        -5        -7
6.740·10  - 8.7·10
————————————————————
           3
   2.672·10 + 5.8
function F(x,y,z,w) { with(Math) {
u = (x-y)/(z+w)
return u
}}

F(x,y,z,w) = (2.4845 ± 0.0009)·10−8