5. If u and v be both functions of the same function of x and

y, prove that

6. If V=ƒ(u, v), u=fi(x, y), v=f2(x, y), show how to find

Ex. Given u = x2 + y2, v = 2xy, show that

12. Prove V2 = m(m + 1),−2.

13. If u and u be functions of x, y, z, both satisfying V2 V = 0,

14. If V, be a homogeneous function of the nth degree,

29. If Pdx+Qdy be a perfect differential of some function

30. If Pdx+Qdy + Rdz can be made a perfect differential of some function of x, y, z by multiplying each term by a common factor, show that

P(DQM) + Q(CRF) +R(DH) -0.

Əz

OR

by

ƏR ƏP
Əz

ду дх

APPLICATIONS TO PLANE CURVES.