1.

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

Answer»

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.


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