Example 24 - Find approx change in volume V of a cube of side x - Finding approximate value- Statement questions

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 24 Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%. Let side of the cube = x metres Increase in side = 2% = 0.02 x Hence ∆𝑥 = 0.02 x Volume of the cube = V = x3 m3 We need to find approximate change in volume of the cube i.e. ∆𝑉 Now, ∆𝑉 = ﷐𝑑𝑣﷮𝑑𝑥﷯∆𝑥 = ﷐𝑑(﷐𝑥﷮3﷯)﷮𝑑𝑥﷯ ∆𝑥 = 3x2 (0.02x) = 0.06x3 Hence, the approximate change in the volume of the cube is 0.06 x3 m3.

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