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

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

If l_(m,n)=intx^(m)cosnxdx, then prove that l_(m,n)=(x^(m)sinnx)/(n)+(mx^(m-1)cosnx)/(n^(2))-(m(m-1))/(n^(2))l_(m-2,n)

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")_(xvec 0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/xi se q u a lto 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))

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|))

Find the square root of (m^(n^(2))n^(m^(2))a^((m+n)))/((m+n)^((m+n)^(2) (i) (m^n)(n^m)a^((m+n)/2) (ii) ((m^(n^2))(n^(m^2))a^((m+n)/2))/(m+n)^(((m+n)^2)/2) (iii) (m^n)(n^m)a^(sqrt(m+n))/(m+n)^(((m+n))) (iv)none of these

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)