A function `f` is defined by `f(x)=|x|^m|x-1|^nAAx in Rdot` The local maximum value of the function is `(m ,n in N)` (a) `1` (b) `m^n.n^m` (c)`(m^m n^n)/((m+n)^(m+n))` (d) `((m n)^(m n))/((m+n)^(m+n))`

The minimum value of the fuction f(x) given by f(x)=(x^m)/(m)+(x^(-n))/(n) " where " 1/m+1/n =1" and " m gt 1 is

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))

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

The value of (m+n)^2+(m-n)^2 is:

Simplify : ((a^(m))/(a^(n)))^(m+n)((a^(n))/(a^(l)))^(n+l)((a^(l))/(a^(m)))^(l+m)

2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5) +..} is equals to

The number of ways in which we can distribute m n students equally among m sections is given by a. ((m n !))/(n !) b. ((m n)!)/((n !)^m) c. ((m n)!)/(m ! n !) d. (m n)^m

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

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

If the only point of inflection of the function f(x)-(x-a)^m(x-b)^n , m, n e N and m!=n is at x=a then