Question

If a is equal to x cube relative error in a would be how many times the relative error in x

Answer 1

It is given that, a = x³

we have to find the relation between relative error of a and relative error of x.

expression, a = x³

taking log both sides,

loga = logx³

or, loga = 3logx [ as we know, logsⁿ = nlogs ]

differentiating both sides,

or, da/a =3 × dx/x

if da comparable to a then, da → ∆a and similarly dx → ∆x

so, ∆a/a = 3 × ∆x/x

hence, relative error in a = 3 × relative error in x.

Answer 2

Answer:

3 times

Step-by-step explanation:

If a is equal to x cube relative error in a would be how many times the relative error in x

a = x³

Δx error in x

Δa = error in a

a = x³

=> Δa/a = 3Δx/x

relative error in a would be 3 times the relative error in x