Q9 of 168 Page 216

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

It is given that the volume of a cube (V) of a side x

⇒ V = x³

⇒ dV =

= (3x²)Δx

= (3x²)(0.03x)

= 0.09x³

Therefore, the approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is 0.09x³.

If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.

If f(x) = 3x² + 15x + 5, then the approximate value of f (3.02) is

Find the maximum and minimum values, if any, of the following functions given by

f (x) = (2x – 1)² + 3

Find the maximum and minimum values, if any, of the following functions given by

f (x) = 9x² + 12x + 2