[m^(2)-n^(2))y_(n)=0],[" ¿valuate: "lit((1+x)^(x)-e)/(x)]

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

The function f (x)={((x ^(2n)))/((x ^(2n) sgn x)^(2n+1))((e ^(1/x)-e ^(-1/x))/(e ^(1/x)+e ^(-(1)/(x))))x ne0 n in N is:

The function f (x)={((x ^(2n)))/((x ^(2n) sgn x)^(2n+1))((e ^(1/x)-e ^(-1/x))/(e ^(1/x)+e ^(-(1)/(x))))x ne0 n in N is:

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

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

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

2cos theta=x+(1)/(x) and 2cos phi=y+(1)/(y) then (A)x^(n)+(1)/(x^(n))=2cos(n theta)n in Z(B)(x)/(y)+(y)/(x)=2cos(theta-phi)(C)xy+(1)/(Xy)=2cos(theta+phi)(D)x^(m)y^(n)+(1)/(x^(m)y^(n))=2(cos m theta+n phi),m,n in Z

Solve the following simultaneous equations for x and y : m(x+y)+n(x-y)-(m^(2)+mn+n^(2))=0, n(x+y)+m(x-y)-(m^(2)-mn+n^(2))=0

If x^(m)y^(n)=(x+y)^(m+n), then ((dy)/(dx))_(x=1,y=2) is equal to

If f(x) = lim_(n->oo) tan^(-1) (4n^2(1-cos(x/n))) and g(x) = lim_(n->oo) n^2/2 ln cos(2x/n) then lim_(x->0) (e^(-2g(x)) -e^(f(x)))/(x^6) equals