Let m and n be two positive integers greater than 1.If `lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2)` then the value of `m/n` is

Let m and n be two positive integers greater than 1. If lim_(alpha rarr0)(e^(cos alpha^(n))-e)/(alpha^(m))=-((e)/(2)) then the value of (m)/(n) is

Let m and n be the two positive integers greater than 1 . If underset( alpha rarr 0 ) ( "lim")((e^(cos(alpha^(n)))-e)/(alpha^(m))) = -((e )/( 2)) then the value of ( m )/( n ) is

lim_(x rarr0)(e^(cos x^(n))-e)/(x^(m))=-(e)/(2) then find (4m)/(5n)

If cot alpha+tan alpha=m and (1)/(cos alpha)-cos alpha=n, then

If and n are positive integers,then lim_(x rarr0)((cos x)^((m)/(m))-(cos x)^((pi)/(n)))/(x^(2)) equal to

If underset(n to oo)lim (1-(10)^(n))/(1+(10)^(n+1))=- alpha/10, then the value of alpha is

If m and n are the smallest positive integers satisfying the relation (2*e^(i(pi)/(6)))^(m)=(4*e^(i(pi)/(4)))^(n), then (m+n) has the value equal to

Let alpha,beta denote the cube roots of unity other than 1 and alpha!=beta. Let S=sum_(n=0)^(302)(-1)^(n)((alpha)/(beta))^(n). Then,the value of S is