A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:
(i) change in the volume
(ii) change in the surface area

The time T, taken for a complete oscillation of a single pendulum with length l, is given by the equation T = 2ㅠ\(\sqrt { \frac { 1 }{ g } } \), where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l.

Show that the percentage error in the n^th root of a number is approximately \(\frac1n\) times the percentage error in the number.

Let f, g : (a, b)→R be differentiable functions. Show that d(fg) = fdg + gdf

Find df for f(x) = x² + 3x and evaluate it for
x = 3 and dx = 0.02