EXERCISE . . Find the asymptotes of the following curves : (i) f x ( ) = (ii) f x ( ) = (iii) f x ( ) = (iv) f x ( ) = (v) f x ( ) = . Sketch the graphs of the following functions: (i) y = − (ii) y (iii) y (iv) y e x = + Fig.
. x = – x = - - EXERCISE . Choose the correct or the most suitable answer from the given four alternatives : . The volume of a sphere is increasing in volume at the rate of p cm / sec .
The rate of change of its radius when radius is cm ( ) cm/s ( ) cm/s ( ) cm/s ( ) cm/s . A balloon rises straight up at m/s. An observer is m away from the spot where the balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per second when the balloon is metres above the ground.
( ) radians/sec ( ) radians/sec ( ) radians/sec ( ) radians/sec . The position of a particle moving along a horizontal line of any time t is given by s t ( ) = . The time at which the particle is at rest is ( ) t = ( ) t = ( ) t = ( ) t = . A stone is thrown up vertically.
The height it reaches at time t seconds is given by x . The stone reaches the maximum height in time t seconds is given by ( ) ( ) . ( ) ( ) . .
The point on the curve at which y -coordinate changes times as fast as x -coordinate is ( ) ( , ( ) ( , ( ) ( − ( ) ( . The abscissa of the point on the curve f x ( ) = at