Question

Find the relative error of y ,if y=x3

Answer 1

not sure about my answer......

Answer 2

Explanation:

y=x

n

⇒

dx

dy

=nx

n−1

Approximate error in y is dy=(

dx

dy

)Δx

=nx

n−1

Δx

Relative error in y is

y

dy

=

x

n

Δx

Approximate error in x is dx=(

dy

dx

)Δy

=

nx

n−1

1

Δy

Relative error in x is

x

dx

=

nx

n

1

Δy

Required ratio =

nx

n

1

Δy

x

n

Δx

=n

2

x

n−1

Δy

Δx

=

1

n

So, the ratio of relative errors in y and x is n:1.