increases from 4 to 4.05 units. Compare the change in volume of the cone with an

approximation of this change using a total differential.

Answer any 2 complete questions each having 7 marks

20.The temperature in degree Celsius at a point in the (x, y) plane is

T xy
T(x, ೫) = ‏سس سے‎
52) 120 + y 2

Find the rate of change of temperature at (1,1) in the direction of (21--)).

21.Find the scalar tangential and normal components of acceleration at time t of a

particle with position vector at time tis r(t) = ti + 12] + 13८
22. Find the equation of the tangent plane and parametric equation for the normal

line 10 the surface ‏خر‎ + y’ +z’ = 25 at P(3,0,4)
Answer any 2 complete questions each having 7 marks

23.Evaluate [[sineaa where R is the region in the first quadrant that is outside the
R

circle 7 = 2 and inside the cardioid ‏م‎ = 2(1+ ००५७)

24.Find the J acobian 2٢لک‎ where x = 4u + v, y=u-2w,
8 ),,۷(

Z=vtw.

25.By changing the order of integration evaluate || 0 ‏ور‎ dy dx