Mat Assign

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Mat Assign
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Assignment - 1 Module-1 1.   Show that if it is possible to draw three normals from the point (a,0)to the parabola 2  y x    shown in the diagram, then a must be greater than ½. One of the normalsis the x-axis. For what values of a are the order other two normals perpendicular? 2.   Find the equation of the normal to the curve  y  x y x   where it cuts the x axis. 3.   Two cars start out 500 miles apart. Car A is to the west of car B and starts driving to the east at 35 mph and at the same time car B starts driving south at 50 mph. After 3 hours of driving at what rate is the distance between the cars changing. Is it increasing or decreasing? 4.   A boy starts walking north at a speed of 1.5 m/s, and a girl starts walking west at the same point P at the same time at a speed of 2 m/s. At what rate is the distance between the boy and the girl increasing 6 seconds later? 5.   1221111 432222   x x xdxdythat  show x x x x yif   Module- 2 6.   Find the shortest distance from the point (1 + n, 0) to the curve ,0 n  yxn    7.   The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the shape of the largest beam that can be cut from a log of given size. 8.   Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides. 9.   Show that 53 ()4712  fxxxx      assumes the value ‘9’ exactly once. 10.   When x is measured in degrees, what is the maximum slope possible for the curve y=sin(x) in the interval [30,60]   .   Module- 3 11.   Find the area below 2 43  yxx     and above 32 7105  yxxx      over the interval 12  x   . 12.   Find the volume of a pyramid with a square base that is 20 meters tall and 20 meters on a side at the base. 13.   Find the volume of the object generated when the area between y = x 2  and y = x is rotated around the x-axis. 14.   Find the area of the region enclosed by the curves  f (  x ) = cos  x and  g (  x ) = cos  x - sin  x over the interval [0,   ]. 15.   Find the area of the region enclosed by the curves f(x) = 2  x e  and g(x) = 2  x e   and h(x)= 1/e. 16.   Evaluate i. ii.
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