Question

If y = a/b, then absolute error in y is​

Answer 1

given equation, y = a/b

taking log both sides,

logy = log(a/b)

• from logarithmic property, log(m/n)=logm - logn

so, logy = loga - logb

or, differentiating both sides,

dy/y = da/a - db/b

if we to find error in y, then place positive sign on right side in place of negative sign. [ it is because , we always assume our finding should be maximum ]

so, dy/y = da/a + db/b

if dy is comparable to y then, dy→ ∆y

similarly, da → ∆a and db →∆b

hence, ∆y/y = ∆a/a + ∆b/b

or, ∆y = y(∆a/a + ∆b/b)

hence, absolute error in y = y(∆a/a + ∆b/b)

or, absolute error in y = y (fractional error of a + fractional error of b)