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

lim_(alpha to 0) (sin (alpha^n))/((sin alpha)^(m))

lim_(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))

alpha beta x ^(alpha-1) e^(-beta x ^(alpha))

Determine a positive integer nlt=5 such that int_0^1e^x(x-1)^n=16-6e

Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if a_n=alpha^n-beta^n for n>=1 then the value of (a_10 - 2a_8)/(2a_9)

Find the value of alpha so that lim_(x->0)1/(x^2)(e^(alphax)-e^x-x)=3/2

If alpha=^m C_2,t h e n^(alpha)C_2 is equal to

Integrate the following with respect to x . alphabetax^(alpha-1)e^(-betax^(alpha))

Let A_(r) be the area of the region bounded between the curves y^(2)=(e^(-kr))x("where "k gt0,r in N)" and the line "y=mx ("where "m ne 0) , k and m are some constants lim_(n to oo)Sigma_(i=1)^(n)A_(i)=(1)/(48(e^(2k)-1)) then the value of m is

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n dn , we have T_m=1//n^2 and T_n=1//m^2 , then find the value of T_(m+n//2.)