EXERCISE 8.1

. Let f x ( ) = . Find the linear approximation at x = . Use the linear approximation to approximate .

. . Use the linear approximation to find approximate values of (i) ( (ii) (iii) . Find a linear approximation for the following functions at the indicated points.

(i) f x (ii) g x = − (iii) h x . The radius of a circular plate is measured as cm instead of the actual length . cm. find the following in calculating change in the area of the circular plate: (i) Absolute error (ii) Relative error (iii) Percentage error .

A sphere is made of ice having radius cm. Its radius decreases from cm to . 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 simple pendulum with length l , is given by the equation T l g = p , where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of percent in the value of l . . Show that the percentage error in the n th root of a number is approximately n times the percentage error in the number