`''(x^(m))^(n)=(x^(n))^(m)''`. Is this equation true ?

lim_(x to a) (x^(m)-a^(m))/(x^(n)-a^(n)) is equal to

The equation (x-n)^(m)+(x-n^(2))^(m)+(x-n^(3))^(m)+....+(x-n^(m))^(m)=0(m is odd positive integer),has

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 m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

lim_(x rarr a)(x^(m)-a^(m))/(x^(n)-a^(n))=((m)/(n))a^(m-n) if m>n

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

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