Ex 6.4,4 - Chapter 6 Class 12 Application of Derivatives

Transcript

Ex 6.4,4 Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 1%. Let side of the cube = x metres Increase in side = 1% = 0.01 x Hence, ∆x = 0.01 x Volume of the cube = V = x3 m3 We need to find approximate change in volume v of the cube i.e. ∆V Now, ∆V = 𝑑𝑣﷮𝑑𝑥﷯ ∆x = 𝑑( 𝑥﷮3﷯)﷮𝑑𝑥﷯ ∆x = 3x2 (0.01x) = 0.003 x3 Hence, the approximate change is 0.003 x3 m3.