15.

16.

17.

18.

19.

25.

Answer any 2 complete questions each having 7 marks

. Find the domains of (i) / (७, ») = 4125-1 മ്‌ (10) f(x,y) =In(x—- y”) and describe

them in words.
Find the limit of f (x, y) = —~4as (x,y) (0,0) along (i) the X-axis, (1) the Y- axis (111)

ഥി

the line y = x.
Find the spherical and cylindrical coordinates of the point that has rectangular
coordinates(x,y,z)=(4,-4,4V6)

Answer any 2 complete questions each having 7 marks

Locate all relative maxima, relative minima and saddle point if any,off (x,y) = y? + xy +
4y+ 2x+ 3
Let ரீ be a differentiable fuction of 3 varaiables and suppose that W = f(x —y,y—z,z— x).

Ow , dw | dw
Prove 114, + 7 ‏سم یت‎ 0.
Find the local linear approximation L(x,y) to f(x,y) “ಡ್‌್‌ at the point P(4,3). Compare the
error in approximating “1? by L at the specified point © (3.92, 3.01) with the distance between ए
and Q.

Answer any 2 complete questions each having 7 marks

. Findy(t)where y(t) = 12% *i— 29, ೫0) = 21- 4j, y ൫5 0.
. Find the arc length parametrization of the line x = 1 + t,y = 3 - 21, z=4 + 21 that has the same

direction as the given line and has reference point (1, 3, 4).

. Find the directional derivative of f(x, y) = e*sec ೫ at P (0, 7/4) in the direction of PQ where 0

is the origin.

Answer any 2 complete questions each having 7 marks

. Find the area bounded by the x-axis, 7 27 and x+y=1 using double integration.
24.

Use a triple integral to find the volume of the solid within the cylinder ‏ضر + تر‎ = 9 and
between the planes z = landx+ 2 = 5.

2
Sketch the region of integration and evaluate the integral | 1 ந்‌ dxdy by changing the order

of integration.