Ex 6.4,5 - Chapter 6 Class 12 Application of Derivatives

Transcript

Ex 6.4,5 Find the approximate change in the surface area of a cube of side x meters caused by decreasing the side by 1%. Let side of the cube = x meters. Decrease in side = 1% = − 0.01 x Hence ∆ x = −0.01 x Surface area of the cube = S = 6x2 m2 We need to find the approximate change in the surface area s of the cube that is ∆ S Now. ∆ S = 𝑑𝑠﷮𝑑𝑥﷯ ∆ x = 𝑑 6 𝑥﷮2﷯﷯﷮𝑑𝑥﷯ ∆ x = 12x (−0.01x) = − 0.12x2 Hence, the approximate change is 0.12x2 m2.