Question

Use differentials to approximate
the value of (33) raise to power 1/5​

Answer 1

(33)

1/5

=(32+1)

1/5

Let y=f(x)=x

1/5

⇒y+Δy=(x+Δx)

1/5

⇒Δy=(x+Δx)

1/5

−x

1/5

Also, Δy=f

′

(x)Δx

⇒(x+Δx)

1/5

−x

1/5

=

5

1

x

−4/5

Δx

Put x=32,Δx=1

(33)

1/5

−(32)

1/5

=

5

1

(2)

−4

(1)

⇒(33)

1/5

=2+0.0125=2.0125

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