If `f(2x+y/8,2x-y/8)=x y` , then `f(m , n)+f(n,m)=0` (a) only when `m=n` (b) only when `m!=n` (c) only when `m=-n` (d) for all m and n

If f(2x+y/8,2x-y/8)=x y , then f(m , n)=0 only when m=n only when m!=n on l yw h e nm=-n (d) fora l lma n dn

Let f(x)=x^(m/n) for x in R where m and n are integers , m even and n odd and 0

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0

If x^m\ y^n=1 , prove that (dy)/(dx)=-(m y)/(n x)

In X-Y plane, the path defined by the equation (1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0 , is (a) a parabola if m = (1)/(2), k =- 1, n =0 (b) a hyperbola if m =1, k =- 1, n=0 (c) a pair of lines if m = k = n =1 (d) a pair of lines if m = k =- 1, n =1

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in Ra n df(1)=5,t h e n f(x)i sa nod dfu n c t ion f(x) is an even function sum_(n=1)^mf(r)=5^(m+1)C_2 sum_(n=1)^mf(r)=(5m(m+2))/3

If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y) , show that : x + y + 2 = 0.

If f(x) = (x^l/x^m)^(l+m) (x^m/x^n)^(m+n) (x^n/x^l)^(n+l) , then find f'(x).