" 0.) "(m)/(n)x^(2)+(n)/(n)=1quad 2x

(m)/(n)x^(2)+(n)/(m)=1-2x

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (a) (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

Show that (n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C_(0))/(x)-(""^(n)C_(1))/(x+1) + (""^(n)C_(2))/(x+2)-(""^(n)C_(3))/(x+3) + ...+ ((-1)^(n)""^(n)C_(n))/(x+n) .

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

f(x)=(a_(2n)x^(2n)+a_(2n-1)x^(2n-1)+...+a_(1)x+a_(0))/(b_(2n)x^(2n)+b_(2n-1)x^(2n-1)+....+b_(1)x+b_(0)) where n in N,a_(i),b_(i)in R and b_(2n!=0). If domain of f(x) is R ,then

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

lim_(x rarr0)((2^(m)+x)^((1)/(m))-(2^(n)+x)^((1)/(n)))/(x) is equal to (1)/(m2^(m))-(1)/(n2^(n)) (b) (1)/(m2^(m))+(1)/(n2^(n))(1)/(m2^(-m))-(1)/(n2^(-n))( d) (1)/(m2^(-m))+(1)/(n2^(-n))

lim_(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

lim_(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to