QUESTION 1 ( x 2 + y2) + sin (x2 +y2) Evaluate lim ( x , y) - (0,0) (x 2 + y2) QUESTION 2 f ( x, y, z) = (x2 + y2 + 1)z, find of (1,1,2) QUESTION 3 f (x,y, z)=(x2 +y2+1)z, find of z (1, 1,2) QUESTION 4 x'y- xy 3 if (x, y) # (0,0) f ( x, y ) = x2+ y 2 0 if (x, y) = (0,0) of evaluate ox (2,0)QUESTION 11 2.0 If z = T(x, y) is an equation of the tangent plane to the 1.8 graph of x- + yz + zz = 3xyz at (1,1,1), write the 1.6 1.4 1.2 value of T Z 1.0 0.8 0.8 0.4 0.8 0.2 0.6 0.0 09 X 1.4 16 18QUESTION 12 Find the directional derivative of f (x,y,z) =x tan '1(yz) at (4,1,1) in the direction of the vector QUESTION 13 Find the maximum value of the directional derivative of f (15,)! ,z) =xe3'z at the point (2,0, 4) QUESTION 14 For f(x,y)=~/'y/ 1+t3dt I find i (2:2) \fQUESTION 8 xy - xy 3 if (x , y) # (0,0) f ( x, y) = x 2+ y2 0 if (x , y) = (0,0) a2f evaluate ayox (0,0) QUESTION 9 x y- xy3 if (x , y) # (0,0) f ( x, y) = x 2 + y 2 0 if (x, y) = (0,0) a2 f evaluate axay ( 0, 0) QUESTION 10 If x2+y2+z2=3xyz oz evaluate ax (1, 1, 1)