Q. f(x,y)= (x^2-y^2)/(x^2+y^2) + x sin(1/(x^2+y^2)) S1:- lim x-->0 y-->0 f(x,y) exists finitely S2:- lim y-->0 x-->0 f(x,y) exists finitely S3:- lim(x,y)-->(0,0) f(x,y) exists finitely A. Both S1,S2,S3 are true B. Both S1,S2 are true but S3 is false C. Both S2,S3 are true but S1 is false D. Both S1,S3 are true but S2 is false
Q. W be the vector space of all bounded solutions of the differential equation D^4 y + 2D^2 y + y=0.Then dimension of W is____(NAT)
M be 6×6 skew symmetric matrix.Then the critical point of the system MX=0 is stable
(A) For all M
(B) For M of rank 4
(C) For M of rank 2
(D) None
Q. f(x,y)= (x^2-y^2)/(x^2+y^2) + x sin(1/(x^2+y^2))
S1:- lim x-->0 y-->0 f(x,y) exists finitely
S2:- lim y-->0 x-->0 f(x,y) exists finitely
S3:- lim(x,y)-->(0,0) f(x,y) exists finitely
A. Both S1,S2,S3 are true
B. Both S1,S2 are true but S3 is false
C. Both S2,S3 are true but S1 is false
D. Both S1,S3 are true but S2 is false