" 2.Show that for a linearly homogenous production function "Q=f(K,L),K*(del Q)/(del K)+L*(del Q)/(del L)-=Q

If f (x,y) is homogeneous function of degree 5 then x (del f)/(delx) +y (del f)/( del y)=

The Cobb-Douglas Production function Q = AL^(a) k^((1a)) is based on

If u is a homogenous function of x and y of degree n, then x(del^(2)u)/(del x^(2)) + y(del^(2)u)/(del x del y) = __________ (del u)/(del x) .

If f=x/(x^(2) + y^(2)) , then show that x (del f)/(del x) + y(del f)/(del y) =-f .

If z=f(x-cy) + F(x+cy) where f and F are any two functions and c is a constant, show that c^(2) (del^(2)z)/(del x^(2)) = (del^(2)z)/(del y^(2)) .

A function f (x,y) is said to be harmonic if (del^(2)f)/(del x ^(2)) + (del^(2)f)/(dely^(2)) =

(i) In a travelling sinusoidal longitudinal wave, the displacement of particle of medium is represented by s = S (x, t) . The midpoint of a compression zone and an adjacent rarefaction zone are represented by letter ‘C’ and ‘R’ respectively. The difference in pressure at ‘C’ and ‘R’ is DeltaP and the bulk modulus of the medium is B. (a) How is |(del s)/(del x)| related to |del/del| (b) Write the value of |(del s)/(del x)|_(C) in terms of DeltaP and B . (c) What is speed of a medium particle located mid-way between ‘C’ and ‘R’. (ii) A standing wave in a pipe with a length of L = 3 m is described by s=A cos ((3pi x)/(L)) sin ((3pi vt)/(L)) where v is wave speed. The atmospheric pressure and density are P_(0) and rho respectively. (a) At t=L/(18v) the acoustic pressure at x =L/2 is 0.2 percent of the atmospheric pressure . Find the displacement amplitude A. (b) In which overtone is the pipe oscillating?

If y=f(x+ct)+g(x-ct), then show that (del^(2)y)/(del t^(2))=c^(2)(del^(2)y)/(del x^(2))